diff --git a/CMakeLists.txt b/CMakeLists.txt index 6825226..8c6082d 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -31,7 +31,7 @@ if(SUPPORTS_FLAG) set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-return-type-c-linkage") endif() -set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O3 -fno-omit-frame-pointer -g -Wall") +set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -DNDEBUG -O3 -fno-omit-frame-pointer -g -Wall") #let gcc take advantage of Eigen3 vectorization if ("${CMAKE_CXX_COMPILER_ID}" STREQUAL "GNU") diff --git a/JamesInput/G_input.dat b/JamesInput/G_input.dat new file mode 100644 index 0000000..4d22595 --- /dev/null +++ b/JamesInput/G_input.dat @@ -0,0 +1,64 @@ +6.283185307179586232e-01 2.235425408254687329e-01 -3.779921571245434264e-02 +1.884955592153875870e+00 1.626491783108343914e-01 -7.435736876643336823e-02 +3.141592653589793116e+00 1.258267416386332216e-01 -9.271123890725486982e-02 +4.398229715025710362e+00 9.492153676237174986e-02 -1.001221458253048202e-01 +5.654866776461627609e+00 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0000000..7d556cc Binary files /dev/null and b/JamesInput/PhysRevB.55.16132.pdf differ diff --git a/JamesInput/SpM.param b/JamesInput/SpM.param new file mode 100644 index 0000000..2e39a0a --- /dev/null +++ b/JamesInput/SpM.param @@ -0,0 +1,12 @@ +BETA = 5 +DATA = ../JamesInput/G_input.dat +DATASPACE =frequency +KERNEL =fermionic +NDAT =64 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =0 +RHO arg =20 +RHOPRIME =2000000 + +LAMBDA =1 diff --git a/JamesInput/SpMselfenergy.nb b/JamesInput/SpMselfenergy.nb new file mode 100644 index 0000000..54450af --- /dev/null +++ b/JamesInput/SpMselfenergy.nb @@ -0,0 +1,1889 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 11.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 96786, 1881] +NotebookOptionsPosition[ 94895, 1812] 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b/JamesInput/b4_correctSigmatau_wrongprocedure/igor/omega2tau.py new file mode 100644 index 0000000..ce84929 --- /dev/null +++ b/JamesInput/b4_correctSigmatau_wrongprocedure/igor/omega2tau.py @@ -0,0 +1,50 @@ +from pytriqs.gf import * +from pytriqs.gf.tools import tail_fit +import numpy as np + +# Read in F(i\omega_n) +f_iw_table = np.loadtxt("selfenergy_17") +freqs = f_iw_table[:,0] +n_iw = len(freqs) +beta = np.pi / freqs[0] + +n_tau = 2049 + +block_names = ("up","dn") + +# F in Matsubara frequency representation +F_iw = BlockGf(name_block_generator = [(bn, GfImFreq(indices=[0], beta = beta, n_points = n_iw)) for bn in block_names], + make_copies = True +) + +F_iw["up"].data[n_iw:,0,0] = f_iw_table[:,1] + 1j*f_iw_table[:,2] +F_iw["up"].data[n_iw-1::-1,0,0] = np.conj(F_iw["up"].data[n_iw:,0,0]) +F_iw["dn"].data[n_iw:,0,0] = f_iw_table[:,3] + 1j*f_iw_table[:,4] +F_iw["dn"].data[n_iw-1::-1,0,0] = np.conj(F_iw["dn"].data[n_iw:,0,0]) + +# Fit tails +for bn, f_iw in F_iw: + f_iw.fit_tail(known_moments = TailGf(1,1,0), + max_moment = 3, + n_min = 400, + n_max = 1024, + replace_by_fit = False) + print "Norm =", f_iw.tail[1][0,0].real + + +# F in imaginary time representation +F_tau = BlockGf(name_block_generator = [(bn, GfImTime(indices=[0], beta = beta, n_points = n_tau)) for bn in block_names], + make_copies = True +) + +# Transform! +for bn, f_iw in F_iw: + F_tau[bn] << InverseFourier(f_iw) + +# Save results +f_tau_table = np.transpose(np.vstack((list(F_tau["up"].mesh), + F_tau["up"].data[:,0,0].real, + F_tau["up"].data[:,0,0].imag, + F_tau["dn"].data[:,0,0].real, + F_tau["dn"].data[:,0,0].imag))) +np.savetxt("selfenergy_17.tau", f_tau_table) diff --git a/JamesInput/b4_correctSigmatau_wrongprocedure/igor/selfenergy_17_1.dat b/JamesInput/b4_correctSigmatau_wrongprocedure/igor/selfenergy_17_1.dat new file mode 100644 index 0000000..2869bbb --- /dev/null +++ b/JamesInput/b4_correctSigmatau_wrongprocedure/igor/selfenergy_17_1.dat @@ -0,0 +1,2049 @@ 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"Gtau.dat" +DATASPACE =time +KERNEL =fermionic +NDAT =1025 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.000001 diff --git a/JamesInput/b50/SpMg0.param b/JamesInput/b50/SpMg0.param new file mode 100644 index 0000000..5dae73e --- /dev/null +++ b/JamesInput/b50/SpMg0.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = "G0tau.dat" +DATASPACE =time +KERNEL =fermionic +NDAT =1024 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.000001 diff --git a/JamesInput/b50/SpMs.param b/JamesInput/b50/SpMs.param new file mode 100644 index 0000000..79eb904 --- /dev/null +++ b/JamesInput/b50/SpMs.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = "Sigmatau.dat" +DATASPACE =time +KERNEL =fermionic +NDAT =2049 +NORM =4 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.000001 diff --git a/JamesInput/b50/krho.dat b/JamesInput/b50/krho.dat new file mode 100644 index 0000000..7426a42 --- /dev/null +++ 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+RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.000001 diff --git a/JamesInput/b50/trial1_wrongndatforGtau_thereforewrongsg_otherwisecorrect/krho.dat b/JamesInput/b50/trial1_wrongndatforGtau_thereforewrongsg_otherwisecorrect/krho.dat new file mode 100644 index 0000000..f1a336c --- /dev/null +++ b/JamesInput/b50/trial1_wrongndatforGtau_thereforewrongsg_otherwisecorrect/krho.dat @@ -0,0 +1,2049 @@ +-0.50000005698269 +-0.44753685245964 +-0.40150373959003 +-0.36102144953858 +-0.32534120214686 +-0.29382410725929 +-0.26592394840674 +-0.24117281888835 +-0.21916913265463 +-0.19956748674615 +-0.18207024411319 +-0.1664204048901 +-0.15239564205393 +-0.13980321101691 +-0.12847570721535 +-0.11826744250482 +-0.10905139842736 +-0.10071659993094 +-0.093165919527982 +-0.086314184338682 +-0.080086577082424 +-0.074417242500237 +-0.069248119378502 +-0.06452792358956 +-0.060211285511039 +-0.056257989126199 +-0.052632333500339 +-0.049302570845009 +-0.046240428297074 +-0.043420680451945 +-0.040820790724248 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1.0000000e+04 9.5783500e-01 3.3925000e-02 3.4020800e+02 + 1.0000000e+05 9.5783500e-01 3.3990800e-02 3.4000400e+03 diff --git a/JamesInput/lambda2/SpM.param b/JamesInput/lambda2/SpM.param new file mode 100644 index 0000000..66b6e66 --- /dev/null +++ b/JamesInput/lambda2/SpM.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = ../G_input.dat +DATASPACE =frequency +KERNEL =fermionic +NDAT =64 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =0 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.00001 diff --git a/JamesInput/lambda2/krho.dat b/JamesInput/lambda2/krho.dat new file mode 100644 index 0000000..585afcf --- /dev/null +++ b/JamesInput/lambda2/krho.dat @@ -0,0 +1,64 @@ +0.20470183421279 +-0.040259016302797 +0.15843072152981 +-0.092109998592786 +0.11118355956574 +-0.10581370331833 +0.078350962069352 +-0.10261841864964 +0.057311797402025 +-0.094929288658397 +0.043740030392415 +-0.08710297471852 +0.034709382685341 +-0.080333914180548 +0.028483323844901 +-0.074789354489639 +0.024043592874127 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+540.83 145.444 L +S +GR +GS +0.149 GC +2 setlinecap +1 LJ +0.5 LW +N +545.5 111.889 M +540.83 111.889 L +S +GR +GS +0.149 GC +2 setlinecap +1 LJ +0.5 LW +N +545.5 78.333 M +540.83 78.333 L +S +GR +GS +0.149 GC +2 setlinecap +1 LJ +0.5 LW +N +545.5 44.778 M +540.83 44.778 L +S +GR +GS +[1 0 0 1 74.3 313.22223] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-7 4 moveto +1 -1 scale +(0) t +GR +GR +GS +[1 0 0 1 74.3 279.66666] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.1) t +GR +GR +GS +[1 0 0 1 74.3 246.11111] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.2) t +GR +GR +GS +[1 0 0 1 74.3 212.55556] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.3) t +GR +GR +GS +[1 0 0 1 74.3 179] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.4) t +GR +GR +GS +[1 0 0 1 74.3 145.44444] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.5) t +GR +GR +GS +[1 0 0 1 74.3 111.88888] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.6) t +GR +GR +GS +[1 0 0 1 74.3 78.33334] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.7) t +GR +GR +GS +[1 0 0 1 74.3 44.77777] CT +0.149 GC +/Helvetica 11 F +GS +[1 0 0 1 0 0] CT +-16 4 moveto +1 -1 scale +(0.8) t +GR +GR +GS +[1 0 0 1 161 22] CT +/Helvetica-Bold 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(A\() t +GR +GR +GS +[1 0 0 1 179 22] CT +/mwa_cmmi10 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(!) t +GR +GR +GS +[1 0 0 1 192 22] CT +/Helvetica-Bold 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(\) Sector, ) t +GR +GR +GS +[1 0 0 1 270 22] CT +/mwb_cmmi10 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(-) t +GR +GR +GS +[1 0 0 1 282 22] CT +/Helvetica-Bold 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +( = 50, ) t +GR +GR +GS +[1 0 0 1 333 22] CT +/mwb_cmmi10 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(;) t +GR +GR +GS +[1 0 0 1 344 22] CT +/Helvetica-Bold 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +( = 20, ) t +GR +GR +GS +[1 0 0 1 395 22] CT +/mwb_cmmi10 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(;) t +GR +GR +GS +[1 0 0 1 406 16] CT +/mwa_cmsy10 14 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +(0) t +GR +GR +GS +[1 0 0 1 411 22] CT +/Helvetica-Bold 18 F +GS +[1 0 0 1 0 0] CT +0 0 moveto +1 -1 scale +( = 200) t +GR +GR +GS +0 1 1 RC +1 LJ +2 LW +N +78.5 313.222 M +79.084 313.222 L +79.667 313.222 L +80.251 313.222 L +80.835 313.222 L +81.419 313.222 L +82.002 313.222 L +82.586 313.222 L +83.17 313.222 L +83.754 313.222 L +84.337 313.222 L +84.921 313.222 L +85.505 313.222 L +86.089 313.222 L +86.673 313.222 L +87.256 313.222 L +87.84 313.222 L +88.424 313.222 L +89.008 313.222 L +89.591 313.222 L +90.175 313.222 L +90.759 313.222 L +91.342 313.222 L +91.926 313.222 L +92.51 313.222 L +93.094 313.222 L +93.677 313.222 L 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Exp. 2011 (05) + [] + + +Underfull \hbox (badness 1436) in paragraph at lines 125--126 +\OT1/cmr/m/n/10 (2011) P05001. arXiv:1101.2646, doi:10.1088/1742- + [] + + +Underfull \hbox (badness 3364) in paragraph at lines 132--133 +[]\OT1/cmr/m/n/12 Analytical con-tin-u-a-tion has been a long- + [] + +[1{/usr/local/texlive/2016/texmf-var/fonts/map/pdftex/updmap/pdftex.map} + + +] +Underfull \hbox (badness 1448) in paragraph at lines 179--181 +\OT1/cmr/m/n/12 Here $\OMS/cmsy/m/n/12 jj^^Ajj[]$ \OT1/cmr/m/n/12 de-notes the +$\OML/cmm/m/it/12 L[]$ \OT1/cmr/m/n/12 norm, de-fined as + [] + +[2] + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `math shift' on input line 201. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `subscript' on input line 201. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `math shift' on input line 201. + +No file spm.bbl. + +Package natbib Warning: There were undefined citations. + +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 273. +[3] +Package atveryend Info: Empty hook `AfterLastShipout' on input line 273. + (./spm.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 273. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 273. +Package rerunfilecheck Info: File `spm.out' has not changed. +(rerunfilecheck) Checksum: 6EB4D6556575FEC8E597927691AFF9DC;349. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 273. + ) +Here is how much of TeX's memory you used: + 9801 strings out of 493014 + 143261 string characters out of 6133351 + 252546 words of memory out of 5000000 + 13164 multiletter control sequences out of 15000+600000 + 15844 words of font info for 59 fonts, out of 8000000 for 9000 + 1143 hyphenation exceptions out of 8191 + 44i,11n,42p,653b,322s stack positions out of 5000i,500n,10000p,200000b,80000s + +< +/usr/local/texlive/2016/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi12.pfb> +Output written on spm.pdf (3 pages, 218351 bytes). +PDF statistics: + 162 PDF objects out of 1000 (max. 8388607) + 137 compressed objects within 2 object streams + 34 named destinations out of 1000 (max. 500000) + 49 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/draft/spm.pdf b/draft/spm.pdf new file mode 100644 index 0000000..b5ad34c Binary files /dev/null and b/draft/spm.pdf differ diff --git a/draft/spm.spl b/draft/spm.spl new file mode 100644 index 0000000..404f503 --- /dev/null +++ b/draft/spm.spl @@ -0,0 +1 @@ +\g@addto@macro\@biboptions{,sort&compress} diff --git a/draft/spm.synctex.gz b/draft/spm.synctex.gz new file mode 100644 index 0000000..9eb5de8 Binary files /dev/null and b/draft/spm.synctex.gz differ diff --git a/draft/spm.tex b/draft/spm.tex new file mode 100644 index 0000000..6748644 --- /dev/null +++ b/draft/spm.tex @@ -0,0 +1,277 @@ +\documentclass[final,5p,twocolumn,12pt]{elsarticle} + +\usepackage{graphicx} +\usepackage{amssymb} +\usepackage{amsmath} + +\biboptions{sort&compress} + +\usepackage{listings} +\lstset{ +basicstyle=\small\ttfamily, +columns=flexible, +breaklines=true +} +\usepackage{fancybox} +\newcommand{\code}[1]{\texttt{#1}} +\PassOptionsToPackage{normalem}{ulem} +\usepackage{ulem} +\usepackage{subfig} +\usepackage{multirow} +%prevent alps[core] hyphenation +\hyphenation{ALPSCore} +\hyphenation{ALPS} + +\usepackage{colortbl} +\definecolor{lightgray}{gray}{0.8} + +\newcounter{bla} +\newenvironment{refnummer}{% +\list{[\arabic{bla}]}% +{\usecounter{bla}% + \setlength{\itemindent}{0pt}% + \setlength{\topsep}{0pt}% + \setlength{\itemsep}{0pt}% + \setlength{\labelsep}{2pt}% + \setlength{\listparindent}{0pt}% + \settowidth{\labelwidth}{[9]}% + \setlength{\leftmargin}{\labelwidth}% + \addtolength{\leftmargin}{\labelsep}% + \setlength{\rightmargin}{0pt}}} + {\endlist} + +\usepackage{hyperref} + +\journal{Computer Physics Communications} + +\begin{document} + +\newcommand{\ME}{\begin{tt}Maxent\end{tt}} +\newcommand{\MEsp}{\begin{tt}Maxent\end{tt} } +\begin{frontmatter} + +\title{Implementation of the Sparse Modeling Method for Analytical Continuation} + +%% use optional labels to link authors explicitly to addresses: +%% \author[label1,label2]{} +%% \address[label1]{
} +%% \address[label2]{
} + +\author[a]{Tianran Chen\corref{author}} +%\author[a,b]{Second Author} +\author[b]{Emanuel Gull} + +\cortext[author] {Corresponding author.\\\textit{E-mail address:} tchen@wcupa.edu} +\address[a]{Department of Physics, West Chester University, PA 19380, USA} +\address[b]{Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA} + +\begin{abstract} +We present SpM, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the `Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv3 and extensively documented. This paper shows the use of the programs in detail. +\end{abstract} + +\begin{keyword} +Sparse Modeling Method \sep Analytic Continuation +\end{keyword} + +\end{frontmatter} + +%% +%% Start line numbering here if you want +%% +% \linenumbers + +% Computer program descriptions should contain the following +% PROGRAM SUMMARY. + +{\bf PROGRAM SUMMARY} + %Delete as appropriate. + +\begin{small} +\noindent +{\em Manuscript Title: } Implementation of the Sparse Modeling Method for Analytic Continuation \\ +{\em Authors: } Tianran Chen and Emanuel Gull \\ +{\em Program Title: } SpM \\ +{\em Journal Reference:} \\ + %Leave blank, supplied by Elsevier. +{\em Catalogue identifier:} \\ + %Leave blank, supplied by Elsevier. +{\em Licensing provisions:} GPLv3 \\ + %enter "none" if CPC non-profit use license is sufficient. +{\em Programming language: C++} \\ +{\em Operating system:} Tested on Linux and Mac OS X \\ + %Operating system(s) for which program has been designed. +{\em RAM:} 10 MB -- 200 MB \\ + %RAM in bytes required to execute program with typical data. +{\em Keywords:} Maximum Entropy Method, Analytic Continuation \\ + % Please give some freely chosen keywords that we can use in a + % cumulative keyword index. +{\em Classification:} 4.9 \\ + %Classify using CPC Program Library Subject Index, see ( + % http://cpc.cs.qub.ac.uk/subjectIndex/SUBJECT_index.html) + %e.g. 4.4 Feynman diagrams, 5 Computer Algebra. +{\em External routines/libraries:} ALPSCore \citep{ALPS20}\cite{ALPSCore}, GSL, HDF5 \\ + % Fill in if necessary, otherwise leave out. +{\em Nature of problem: +}The analytic continuation of imaginary axis correlation functions to real frequency/time variables is an ill-posed problem which has an infinite number of solutions. \\ + %Describe the nature of the problem here. + \\ +{\em Solution method: }The sparse modeling method obtains a possible solution that maximizes entropy, enforces sum rules, and otherwise produces `smooth' curves. Our implementation allows for input in Matsubara frequencies, imaginary time, or a Legendre expansion. It implements a range of bosonic, fermionic and generalized kernels for normal and anomalous Green's functions, self-energies, and two-particle response functions.\\ + %Describe the method solution here. + \\ +{\em Running time: }10s - 2h per solution\\ + %Give an indication of the typical running time here. + \\ +\begin{thebibliography}{0} +\bibitem{1}B. Bauer, et al., The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. Theor. Exp. 2011 (05) (2011) P05001. arXiv:1101.2646, doi:10.1088/1742-5468/2011/ 05/P05001. +\bibitem{2}A. Gaenko, E. Gull, A. E. Antipov, L. Gamper, G. Carcassi, J. Paki, R. Levy, M. Dolfi, J. Greitemann, J.P.F. LeBlanc, Alpscore: Version 0.5.4doi: 10.5281/zenodo.50203. +\end{thebibliography} +\end{small} + +%% main text +\section{Introduction} +Analytical continuation has been a long-standing problem in quantum many-body physics. In numerical simulations of many-body systems such as quantum Monte Carlo lattice and impurity solvers, correlation functions are usually calculated in the imaginary time formalism; in experiments, however, it's the real frequency response or spectral functions that are measured. To compare with experimental results, one needs to use analytical continuation to convert the numerical data from imaginary to real axis. + +Analytical continuation, however, is very sensitive to noise, especially for quantum Monte Carlo (QMC) simulations. Any small fluctuations in the input data, such as Monte Carlo statistical noise or finite precision, may lead to large fluctuations of the output data. For this reason, the standard Pade approximation often generates unphysical solutions. To reduce sensitivity to noise, a variety of alternatives have been proposed, including the maximum entropy method [ref], a constrained optimization procedure [ref], and a number of stochastic methods [ref]. + +In this paper, we will discuss a more recent algorithm: sparse modeling (SpM), which utilizes some of the new techniques developed in data science and information theories. Compared to other methods, SpM proves to have the advantage of obtaining stable and physical real-frequency spectra, by eliminating the redundant variables that may cause overfitting. In the remainder of the paper, we will briefly review the formalism of SpM method and introduce its implementation with examples. Our implementation is part of the ALPS applications and makes use of the core ALPS libraries. + +\section{Sparse Modeling Approach} +\subsection{Analytical Continuation} +In diagrammatic perturbation theory and quantum Monte Carlo simulations, Green's function is computed in the imaginary time as $G(\tau)$, with $0<\tau<\beta$, or in the imaginary frequency as $G(i\omega_n)$ through a Fourier transform: + +\begin{equation} +G(i\omega_n)=\int_0^\beta e^{i\omega_n\tau}G(\tau), +\end{equation} +where $i\omega_n$ are the Matsubara frequencies: $i\omega_n = 2\pi(n+\frac{1}{2})/\beta$ for fermionic and $i\omega_n=2\pi n/\beta$ for bosonic operators. In the case of fermions, $G(\tau)$ and $G(i\omega_n)$ are related to a real frequency Green's function $G(\omega)$ via +%\begin{equation} +%G(\tau) = \frac{1}{\pi}\int_{-\infty}^{\infty} \frac{d\omega \text{Im}\left[G(\omega)%%%\right]e^{-\tau\omega}}{1+e^{-\beta\omega}}. \label{taucont} +%\end{equation} +\begin{align} +G(\tau) &= \frac{1}{\pi}\int_{-\infty}^{\infty} \frac{d\omega \thinspace \text{Im}\left[G(\omega)\right]e^{-\tau\omega}}{1+e^{-\beta\omega}}, \label{taucont}\\ +G(i\omega_n) &= \frac{-1}{\pi}\int_{-\infty}^{\infty} \frac{d\omega \thinspace \text{Im}\left[G(\omega)\right]}{i\omega_n - \omega},\label{omegacont} +\end{align} +Defining the spectral function +\begin{equation} +\mathcal{A}(\omega)=-\dfrac{1}{\pi}\mbox{Im}\left[G(\omega)\right], +\end{equation} +one can formulate Eq.~\ref{taucont} as +\begin{equation} +G(\tau)=\int_{-\infty}^{\infty} d\omega\thinspace K(\tau,\omega)\mathcal{A}(\omega), +\label{eq:G=KA} +\end{equation} +where $0\leq\tau\leq\beta\equiv1/T$, and the kernel $K(\tau,\omega)$ is given by +\begin{equation} +K(\tau,\omega) =-\dfrac{e^{-\tau\omega}}{1+e^{-\omega\beta}}. +\end{equation} +In analytical continuation, the imaginary time Green's function $G(\tau)$ produced from QMC simulations is the input data, while $\mathcal{A}(\omega)$, the desired real frequency spectral function, is the output data. Thus, analytical continuation is essentially an inversion problem: for a given input $G(\tau)$, one can infer $\mathcal{A}(\omega)$ from the inverse of the integral. + +However, due to the bad conditioning of kernel $K(\tau,\omega)$, Eq.~\ref{eq:G=KA} becomes very sensitive to noise: even tiny fluctuations in $G(\tau)$ may lead to large variations of $\mathcal{A}(\omega)$, making it difficult to select the reasonable solution among a large number of possible spectra. + +Thus, instead of solving the spectral function exactly, an alternative way is to minimize the deviation between an approximate $\mathcal{A}$ and the original input $G$. For simplicity, we write Eq.~\ref{eq:G=KA} as a linear vector equation: +\begin{equation} +\boldsymbol G=K\boldsymbol{\mathcal{A}} +\label{G=KA} +\end{equation} +where $G_i\equiv G(\tau_i)$, $K_{ij}\equiv K(\tau_i,\omega_j)$, and $\mathcal{A}_j \equiv \mathcal{A}(\omega_j)\Delta\omega$. Here, $\tau$ is discretized to $M$ points in the range of $[0:\beta]$, while $\omega$ is discretized to $N$ points in the range of $[-\omega_{max}:\omega_{max}]$. The discretization can be in linear or non-linear manner. One can characterize the deviation between the approximated $\mathcal{A}$ and the original input data as +\begin{equation} +\chi^2=\frac{1}{2}\lvert\lvert \boldsymbol G-K\boldsymbol{\mathcal{A}} \rvert\rvert^{2}_{2}. +\label{chi2} +\end{equation} +Here $\lvert\lvert\cdot\rvert\rvert_2$ denotes the $L_2$ norm, defined as $\lvert\lvert \boldsymbol{\mathcal{A}}\rvert\rvert_2\equiv (\sum_j\mathcal{A}^2_j)^{1/2}$. To find the solution, one needs to optimize Eq.~\ref{chi2}. + +Because $\boldsymbol{\mathcal{A}}$ is a spectral function, the optimization of $\chi^2$ is subject to two physical constraints: $\boldsymbol{\mathcal{A}}$ is exclusively positive and integrates to one: +\begin{align} +&\mathcal{A}_j \geq 0 \thinspace \thinspace \forall j, \label{positivity}\\ +&\sum_j\mathcal{A}_j=1. \label{norm} +\end{align} + +\subsection{SVD} +Since matrix $K$ is ill-conditioned and difficult to invert, one can use the singular value decomposition (SVD) to decompose $K$ into: +\begin{equation} +K=USV^t, +\label{svd} +\end{equation} +where $S$ is an $M\times N$ diagonal matrix, and $U$ and $V$ are orthogonal matrices of size $M\times M$ and $N\times N$, respectively. [This way the matrix $S$ can be compressed suitably by removing eigenvalues that are zero within numerical precision. Note: I don't think this is what Hiroshi's paper does.]. With SVD, Eq.~\ref{chi2} becomes +\begin{equation} +\chi^2 := \frac{1}{2}\lvert\lvert U^T \boldsymbol G-SV^T\boldsymbol{\mathcal{A}} \rvert\rvert^{2}_{2} =:\frac{1}{2}\lvert\lvert y'-Sx'\rvert\rvert^{2}_{2}, +\label{chi2v2} +\end{equation} +where $y'=U^T\boldsymbol G$ and $x'=V^T\boldsymbol{\mathcal{A}}$. + +\subsection{$L_1$ regularization} +Because the singular values $s_l(l=0,1,2,\cdots)$ decay exponentially, the corresponding elements of $x'$ in Eq.~\ref{chi2v2} are negligibly small, causing the optimization of $\chi^2$ to be very sensitive to noise. In order to find a stable solution that is independent of noise, the authors of [ref] propose adding an additional term, the so-called $L_1$ norm, to Eq.~\ref{chi2v2}: +\begin{equation} +|x'|_1=\sum_j |x'_j|. +\end{equation} +%where $\lvert\lvert\cdot\rvert\rvert_1$ denotes the $L_1$ norm, defined as $\lvert\lvert \boldsymbol{\rho}'\rvert\rvert_1\equiv \sum_l|\rho'_l|$. +Therefore, one should minimize +\begin{equation} +L_\lambda(x')=\frac{1}{2}\lvert\lvert y'-Sx'\rvert\rvert^{2}_{2} + \lambda|x'|_1, +\label{chi2v3} +\end{equation} +where $\lambda$ is a positive (a priori arbitrary) parameter used to penalize large $|x'|_1$. The $L_1$ norm plays the role of imposing sparseness on $x'$, and therefore helps select the solution among a large number of possible spectra that all satisfy Eq.~\ref{G=KA} within a given accuracy. For more detailed justification of $L_1$ regularization see [ref]. The optimization of Eq.~\ref{chi2v3} is of the form of a LASSO (Least Absolute Shrinkage and Selection Operators) problem with two physical constraints: a convex constraint for the positivity (Eq.~\ref{positivity}), and a constraint for the norm (Eq.~\ref{norm}). + +\subsection{ADMM} +The optimization of Eq.~\ref{chi2v3} without the two physical constraints can be carried out using ADMM as illustrated in [ref]. To minimize Eq.~\ref{chi2v3}, it is equivalent to do the following: +\begin{align} +&\text{minimize } \thinspace f(x')+g(z') \\ +&\text{subject to } \thinspace x'-z'=0, +\end{align} +where we define +\begin{align} +&f(x')=\frac{1}{2}\lvert\lvert y'-Sx'\rvert\rvert^{2}_{2} \\ +&g(z')=\lambda|z'|_1. +\end{align} +The ADMM algorithm solves the optimization problem of the above form by forming an augmented Lagrangian with parameter $\rho$ +\begin{equation} +\begin{aligned} +L_\rho(x,z,y)=f(x)+g(z)+y^T(Ax+Bz-c) \\ ++ \frac{\rho}{2}\lvert\lvert Ax+Bz-c'\rvert\rvert^{2}_{2}. +\end{aligned} +\end{equation} +The first two terms are the Lagrangian without the ``augmented'' constraint. The remaining part would be zero if the constraint is satisfied. + +\label{} + +%% The Appendices part is started with the command \appendix; +%% appendix sections are then done as normal sections +%% \appendix + +%% \section{} +%% \label{} + +%% References +%% +%% Following citation commands can be used in the body text: +%% Usage of \cite is as follows: +%% \cite{key} ==>> [#] +%% \cite[chap. 2]{key} ==>> [#, chap. 2] +%% + +%% References with bibTeX database: + +\bibliographystyle{elsarticle-num} +\bibliography{} + +%% Authors are advised to submit their bibtex database files. They are +%% requested to list a bibtex style file in the manuscript if they do +%% not want to use elsarticle-num.bst. + +%% References without bibTeX database: + +% \begin{thebibliography}{00} + +%% \bibitem must have the following form: +%% \bibitem{key}... +%% + +% \bibitem{} + +% \end{thebibliography} + + +\end{document} + +%% +%% End of file + diff --git a/draft/spm_v1.tex b/draft/spm_v1.tex new file mode 100644 index 0000000..b312fb8 --- /dev/null +++ b/draft/spm_v1.tex @@ -0,0 +1,218 @@ +\documentclass[final,5p,twocolumn,12pt]{elsarticle} + +\usepackage{graphicx} +\usepackage{amssymb} +\usepackage{amsmath} + +\biboptions{sort&compress} + +\usepackage{listings} +\lstset{ +basicstyle=\small\ttfamily, +columns=flexible, +breaklines=true +} +\usepackage{fancybox} +\newcommand{\code}[1]{\texttt{#1}} +\PassOptionsToPackage{normalem}{ulem} +\usepackage{ulem} +\usepackage{subfig} +\usepackage{multirow} +%prevent alps[core] hyphenation +\hyphenation{ALPSCore} +\hyphenation{ALPS} + +\usepackage{colortbl} +\definecolor{lightgray}{gray}{0.8} + +\newcounter{bla} +\newenvironment{refnummer}{% +\list{[\arabic{bla}]}% +{\usecounter{bla}% + \setlength{\itemindent}{0pt}% + \setlength{\topsep}{0pt}% + \setlength{\itemsep}{0pt}% + \setlength{\labelsep}{2pt}% + \setlength{\listparindent}{0pt}% + \settowidth{\labelwidth}{[9]}% + \setlength{\leftmargin}{\labelwidth}% + \addtolength{\leftmargin}{\labelsep}% + \setlength{\rightmargin}{0pt}}} + {\endlist} + +\usepackage{hyperref} + +\journal{Computer Physics Communications} + +\begin{document} + +\newcommand{\ME}{\begin{tt}Maxent\end{tt}} +\newcommand{\MEsp}{\begin{tt}Maxent\end{tt} } +\begin{frontmatter} + +\title{Implementation of the Sparse Modeling Method for Analytical Continuation} + +%% use optional labels to link authors explicitly to addresses: +%% \author[label1,label2]{} +%% \address[label1]{
} +%% \address[label2]{
} + +\author[a]{Tianran Chen\corref{author}} +%\author[a,b]{Second Author} +\author[b]{Emanuel Gull} + +\cortext[author] {Corresponding author.\\\textit{E-mail address:} tchen@wcupa.edu} +\address[a]{Department of Physics, West Chester University, PA 19380, USA} +\address[b]{Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA} + +\begin{abstract} +We present SpM, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the `Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv3 and extensively documented. This paper shows the use of the programs in detail. +\end{abstract} + +\begin{keyword} +Sparse Modeling Method \sep Analytic Continuation +\end{keyword} + +\end{frontmatter} + +%% +%% Start line numbering here if you want +%% +% \linenumbers + +% Computer program descriptions should contain the following +% PROGRAM SUMMARY. + +{\bf PROGRAM SUMMARY} + %Delete as appropriate. + +\begin{small} +\noindent +{\em Manuscript Title: } Implementation of the Sparse Modeling Method for Analytic Continuation \\ +{\em Authors: } Tianran Chen and Emanuel Gull \\ +{\em Program Title: } SpM \\ +{\em Journal Reference:} \\ + %Leave blank, supplied by Elsevier. +{\em Catalogue identifier:} \\ + %Leave blank, supplied by Elsevier. +{\em Licensing provisions:} GPLv3 \\ + %enter "none" if CPC non-profit use license is sufficient. +{\em Programming language: C++} \\ +{\em Operating system:} Tested on Linux and Mac OS X \\ + %Operating system(s) for which program has been designed. +{\em RAM:} 10 MB -- 200 MB \\ + %RAM in bytes required to execute program with typical data. +{\em Keywords:} Maximum Entropy Method, Analytic Continuation \\ + % Please give some freely chosen keywords that we can use in a + % cumulative keyword index. +{\em Classification:} 4.9 \\ + %Classify using CPC Program Library Subject Index, see ( + % http://cpc.cs.qub.ac.uk/subjectIndex/SUBJECT_index.html) + %e.g. 4.4 Feynman diagrams, 5 Computer Algebra. +{\em External routines/libraries:} ALPSCore \citep{ALPS20}\cite{ALPSCore}, GSL, HDF5 \\ + % Fill in if necessary, otherwise leave out. +{\em Nature of problem: +}The analytic continuation of imaginary axis correlation functions to real frequency/time variables is an ill-posed problem which has an infinite number of solutions. \\ + %Describe the nature of the problem here. + \\ +{\em Solution method: }The sparse modeling method obtains a possible solution that maximizes entropy, enforces sum rules, and otherwise produces `smooth' curves. Our implementation allows for input in Matsubara frequencies, imaginary time, or a Legendre expansion. It implements a range of bosonic, fermionic and generalized kernels for normal and anomalous Green's functions, self-energies, and two-particle response functions.\\ + %Describe the method solution here. + \\ +{\em Running time: }10s - 2h per solution\\ + %Give an indication of the typical running time here. + \\ +\begin{thebibliography}{0} +\bibitem{1}B. Bauer, et al., The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. Theor. Exp. 2011 (05) (2011) P05001. arXiv:1101.2646, doi:10.1088/1742-5468/2011/ 05/P05001. +\bibitem{2}A. Gaenko, E. Gull, A. E. Antipov, L. Gamper, G. Carcassi, J. Paki, R. Levy, M. Dolfi, J. Greitemann, J.P.F. LeBlanc, Alpscore: Version 0.5.4doi: 10.5281/zenodo.50203. +\end{thebibliography} +\end{small} + +%% main text +\section{Introduction} +Analytical continuation has been a long-standing problem in quantum many-body physics. In numerical simulations of many-body systems such as quantum Monte Carlo lattice and impurity solvers, correlation functions are usually calculated in the imaginary time formalism; in experiments, however, it's the real frequency response or spectral functions that are measured. To compare with experimental results, one needs to use analytical continuation to convert the numerical data from imaginary to real axis. + +Analytical continuation, however, is very sensitive to noise, especially for quantum Monte Carlo (QMC) simulations. Any small fluctuations in the input data, such as Monte Carlo statistical noise or finite precision, may lead to large fluctuations of the output data. For this reason, the standard Pade approximation often generates unphysical solutions. To reduce sensitivity to noise, a variety of alternatives have been proposed, including the maximum entropy method [ref], a constrained optimization procedure [ref], and a number of stochastic methods [ref]. + +In this paper, we will discuss a more recent algorithm: sparse modeling (SpM), which utilizes some of the new techniques developed in data science and information theories. Compared to other methods, SpM proves to have the advantage of obtaining stable and physical real-frequency spectra, by eliminating the redundant variables that may cause overfitting. In the remainder of the paper, we will briefly review the formalism of SpM method and introduce its implementation with examples. Our implementation is part of the ALPS applications and makes use of the core ALPS libraries. + +\section{Sparse Modeling Approach} +\subsection{Analytic Continuation} +In diagrammatic perturbation theory and quantum Monte Carlo simulations, Green's function is computed in the imaginary time as $G(\tau)$, with $0<\tau<\beta$, or in the imaginary frequency as $G(i\omega_n)$ through a Fourier transform: + +\begin{equation} +G(i\omega_n)=\int_0^\beta e^{i\omega_n\tau}G(\tau), +\end{equation} +where $i\omega_n$ are the Matsubara frequencies: $i\omega_n = 2\pi(n+\frac{1}{2})/\beta$ for fermionic and $i\omega_n=2\pi n/\beta$ for bosonic operators. In the case of fermions, $G(\tau)$ is related to a real frequency Green's function $G(\omega)$ via +\begin{equation} +G(\tau) = \frac{1}{\pi}\int_{-\infty}^{\infty} \frac{d\omega \text{Im}\left[G(\omega)\right]e^{-\tau\omega}}{1+e^{-\beta\omega}}. \label{taucont} +\end{equation} +Defining the spectral function +\begin{equation} +\mathcal{A}(\omega)=-\dfrac{1}{\pi}\mbox{Im}\left[G(\omega)\right], +\end{equation} +one can formulate Eq.~\ref{taucont} as +\begin{equation} +G(\tau)=\int_{-\infty}^{\infty} d\omega\thinspace K(\tau,\omega)\mathcal{A}(\omega), +\label{eq:G=KA} +\end{equation} +where $0\leq\tau\leq\beta\equiv1/T$, and the kernel $K(\tau,\omega)$ is given by +\begin{equation} +K(\tau,\omega) =-\dfrac{e^{-\tau\omega}}{1+e^{-\omega\beta}}. +\end{equation} +In analytical continuation, the imaginary time Green's function $G(\tau)$ is the input data (produced from QMC simulations), and $\mathcal{A}(\omega)$, the desired real frequency spectral function, is the output data. Thus, analytical continuation is essentially an inversion problem: for a given input $G(\tau)$, one can infer $\mathcal{A}(\omega)$ from the inverse of the integral. + +However, due to the bad conditioning of kernel $K(\tau,\omega)$, Eq.~\ref{eq:G=KA} becomes very sensitive to noise: even small fluctuations in $G(\tau)$ may lead to large variations of $\mathcal{A}(\omega)$, making it difficult to select the actual solution among a large number of possible spectra. + +Thus, instead of solving for the spectral function exactly, one can approximate it and then evaluate the deviation. For simplicity, we write Eq.~\ref{eq:G=KA} as a linear vector equation: +\begin{equation} +G= K\mathcal{A}, +\end{equation} +where $G_i\equiv G(\tau_i)$, $K_{ij}\equiv K(\tau_i,\omega_j)$, and $\mathcal{A}_j \equiv \mathcal{A}(\omega_j)\Delta\omega$. Here, $\tau$ is discretized in linear or non-linear manner to $M$ points in the range of $[0:\beta]$, while $\omega$ is discretized to $N$ points in $[-\omega_{max}:\omega_{max}]$. + + + + + +\label{} + +%% The Appendices part is started with the command \appendix; +%% appendix sections are then done as normal sections +%% \appendix + +%% \section{} +%% \label{} + +%% References +%% +%% Following citation commands can be used in the body text: +%% Usage of \cite is as follows: +%% \cite{key} ==>> [#] +%% \cite[chap. 2]{key} ==>> [#, chap. 2] +%% + +%% References with bibTeX database: + +\bibliographystyle{elsarticle-num} +\bibliography{} + +%% Authors are advised to submit their bibtex database files. 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} +%% \address[label2]{
} + +\author[a]{Tianran Chen\corref{author}} +%\author[a,b]{Second Author} +\author[b]{Emanuel Gull} + +\cortext[author] {Corresponding author.\\\textit{E-mail address:} tchen@wcupa.edu} +\address[a]{Department of Physics, West Chester University, PA 19380, USA} +\address[b]{Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA} + +\begin{abstract} +We present SpM, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the `Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv3 and extensively documented. This paper shows the use of the programs in detail. +\end{abstract} + +\begin{keyword} +Sparse Modeling Method \sep Analytic Continuation +\end{keyword} + +\end{frontmatter} + +%% +%% Start line numbering here if you want +%% +% \linenumbers + +% Computer program descriptions should contain the following +% PROGRAM SUMMARY. + +{\bf PROGRAM SUMMARY} + %Delete as appropriate. + +\begin{small} +\noindent +{\em Manuscript Title: } Implementation of the Sparse Modeling Method for Analytic Continuation \\ +{\em Authors: } Tianran Chen and Emanuel Gull \\ +{\em Program Title: } SpM \\ +{\em Journal Reference:} \\ + %Leave blank, supplied by Elsevier. +{\em Catalogue identifier:} \\ + %Leave blank, supplied by Elsevier. +{\em Licensing provisions:} GPLv3 \\ + %enter "none" if CPC non-profit use license is sufficient. +{\em Programming language: C++} \\ +{\em Operating system:} Tested on Linux and Mac OS X \\ + %Operating system(s) for which program has been designed. +{\em RAM:} 10 MB -- 200 MB \\ + %RAM in bytes required to execute program with typical data. +{\em Keywords:} Maximum Entropy Method, Analytic Continuation \\ + % Please give some freely chosen keywords that we can use in a + % cumulative keyword index. +{\em Classification:} 4.9 \\ + %Classify using CPC Program Library Subject Index, see ( + % http://cpc.cs.qub.ac.uk/subjectIndex/SUBJECT_index.html) + %e.g. 4.4 Feynman diagrams, 5 Computer Algebra. +{\em External routines/libraries:} ALPSCore \citep{ALPS20}\cite{ALPSCore}, GSL, HDF5 \\ + % Fill in if necessary, otherwise leave out. +{\em Nature of problem: +}The analytic continuation of imaginary axis correlation functions to real frequency/time variables is an ill-posed problem which has an infinite number of solutions. \\ + %Describe the nature of the problem here. + \\ +{\em Solution method: }The sparse modeling method obtains a possible solution that maximizes entropy, enforces sum rules, and otherwise produces `smooth' curves. Our implementation allows for input in Matsubara frequencies, imaginary time, or a Legendre expansion. It implements a range of bosonic, fermionic and generalized kernels for normal and anomalous Green's functions, self-energies, and two-particle response functions.\\ + %Describe the method solution here. + \\ +{\em Running time: }10s - 2h per solution\\ + %Give an indication of the typical running time here. + \\ +\begin{thebibliography}{0} +\bibitem{1}B. Bauer, et al., The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. Theor. Exp. 2011 (05) (2011) P05001. arXiv:1101.2646, doi:10.1088/1742-5468/2011/ 05/P05001. +\bibitem{2}A. Gaenko, E. Gull, A. E. Antipov, L. Gamper, G. Carcassi, J. Paki, R. Levy, M. Dolfi, J. Greitemann, J.P.F. LeBlanc, Alpscore: Version 0.5.4doi: 10.5281/zenodo.50203. +\end{thebibliography} +\end{small} + +%% main text +\section{Introduction} +\label{} + +%% The Appendices part is started with the command \appendix; +%% appendix sections are then done as normal sections +%% \appendix + +%% \section{} +%% \label{} + +%% References +%% +%% Following citation commands can be used in the body text: +%% Usage of \cite is as follows: +%% \cite{key} ==>> [#] +%% \cite[chap. 2]{key} ==>> [#, chap. 2] +%% + +%% References with bibTeX database: + +\bibliographystyle{elsarticle-num} +\bibliography{} + +%% Authors are advised to submit their bibtex database files. 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COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/100000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 10) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#endif + + +#elif defined(__SDCC_VERSION_MAJOR) || defined(SDCC) +# define COMPILER_ID "SDCC" +# if defined(__SDCC_VERSION_MAJOR) +# define COMPILER_VERSION_MAJOR DEC(__SDCC_VERSION_MAJOR) +# define COMPILER_VERSION_MINOR DEC(__SDCC_VERSION_MINOR) +# define COMPILER_VERSION_PATCH DEC(__SDCC_VERSION_PATCH) +# else + /* SDCC = VRP */ +# define COMPILER_VERSION_MAJOR DEC(SDCC/100) +# define COMPILER_VERSION_MINOR DEC(SDCC/10 % 10) +# define COMPILER_VERSION_PATCH DEC(SDCC % 10) +# endif + +#elif defined(_SGI_COMPILER_VERSION) || defined(_COMPILER_VERSION) +# define COMPILER_ID "MIPSpro" +# if defined(_SGI_COMPILER_VERSION) + /* _SGI_COMPILER_VERSION = VRP */ +# define COMPILER_VERSION_MAJOR DEC(_SGI_COMPILER_VERSION/100) +# define COMPILER_VERSION_MINOR DEC(_SGI_COMPILER_VERSION/10 % 10) +# define COMPILER_VERSION_PATCH DEC(_SGI_COMPILER_VERSION % 10) +# else + /* _COMPILER_VERSION = VRP */ +# define COMPILER_VERSION_MAJOR DEC(_COMPILER_VERSION/100) +# define COMPILER_VERSION_MINOR DEC(_COMPILER_VERSION/10 % 10) +# define COMPILER_VERSION_PATCH DEC(_COMPILER_VERSION % 10) +# endif + + +/* These compilers are either not known or too old to define an + identification macro. Try to identify the platform and guess that + it is the native compiler. */ +#elif defined(__sgi) +# define COMPILER_ID "MIPSpro" + +#elif defined(__hpux) || defined(__hpua) +# define COMPILER_ID "HP" + +#else /* unknown compiler */ +# define COMPILER_ID "" +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_compiler = "INFO" ":" "compiler[" COMPILER_ID "]"; +#ifdef SIMULATE_ID +char const* info_simulate = "INFO" ":" "simulate[" SIMULATE_ID "]"; +#endif + +#ifdef __QNXNTO__ +char const* qnxnto = "INFO" ":" "qnxnto[]"; +#endif + +#if defined(__CRAYXE) || defined(__CRAYXC) +char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; +#endif + +#define STRINGIFY_HELPER(X) #X +#define STRINGIFY(X) STRINGIFY_HELPER(X) + +/* Identify known platforms by name. */ +#if defined(__linux) || defined(__linux__) || defined(linux) +# define PLATFORM_ID "Linux" + +#elif defined(__CYGWIN__) +# define PLATFORM_ID "Cygwin" + +#elif defined(__MINGW32__) +# define PLATFORM_ID "MinGW" + +#elif defined(__APPLE__) +# define PLATFORM_ID "Darwin" + +#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32) +# define PLATFORM_ID "Windows" + +#elif defined(__FreeBSD__) || defined(__FreeBSD) +# define PLATFORM_ID "FreeBSD" + +#elif defined(__NetBSD__) || defined(__NetBSD) +# define PLATFORM_ID "NetBSD" + +#elif defined(__OpenBSD__) || defined(__OPENBSD) +# define PLATFORM_ID "OpenBSD" + +#elif defined(__sun) || defined(sun) +# define PLATFORM_ID "SunOS" + +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) +# define PLATFORM_ID "AIX" + +#elif defined(__sgi) || defined(__sgi__) || defined(_SGI) +# define PLATFORM_ID "IRIX" + +#elif defined(__hpux) || defined(__hpux__) +# define PLATFORM_ID "HP-UX" + +#elif defined(__HAIKU__) +# define PLATFORM_ID "Haiku" + +#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS) +# define PLATFORM_ID "BeOS" + +#elif defined(__QNX__) || defined(__QNXNTO__) +# define PLATFORM_ID "QNX" + +#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__) +# define PLATFORM_ID "Tru64" + +#elif defined(__riscos) || defined(__riscos__) +# define PLATFORM_ID "RISCos" + +#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__) +# define PLATFORM_ID "SINIX" + +#elif defined(__UNIX_SV__) +# define PLATFORM_ID "UNIX_SV" + +#elif defined(__bsdos__) +# define PLATFORM_ID "BSDOS" + +#elif defined(_MPRAS) || defined(MPRAS) +# define PLATFORM_ID "MP-RAS" + +#elif defined(__osf) || defined(__osf__) +# define PLATFORM_ID "OSF1" + +#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv) +# define PLATFORM_ID "SCO_SV" + +#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX) +# define PLATFORM_ID "ULTRIX" + +#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX) +# define PLATFORM_ID "Xenix" + +#elif defined(__WATCOMC__) +# if defined(__LINUX__) +# define PLATFORM_ID "Linux" + +# elif defined(__DOS__) +# define PLATFORM_ID "DOS" + +# elif defined(__OS2__) +# define PLATFORM_ID "OS2" + +# elif defined(__WINDOWS__) +# define PLATFORM_ID "Windows3x" + +# else /* unknown platform */ +# define PLATFORM_ID +# endif + +#else /* unknown platform */ +# define PLATFORM_ID + +#endif + +/* For windows compilers MSVC and Intel we can determine + the architecture of the compiler being used. This is because + the compilers do not have flags that can change the architecture, + but rather depend on which compiler is being used +*/ +#if defined(_WIN32) && defined(_MSC_VER) +# if defined(_M_IA64) +# define ARCHITECTURE_ID "IA64" + +# elif defined(_M_X64) || defined(_M_AMD64) +# define ARCHITECTURE_ID "x64" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# elif defined(_M_ARM) +# if _M_ARM == 4 +# define ARCHITECTURE_ID "ARMV4I" +# elif _M_ARM == 5 +# define ARCHITECTURE_ID "ARMV5I" +# else +# define ARCHITECTURE_ID "ARMV" STRINGIFY(_M_ARM) +# endif + +# elif defined(_M_MIPS) +# define ARCHITECTURE_ID "MIPS" + +# elif defined(_M_SH) +# define ARCHITECTURE_ID "SHx" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__WATCOMC__) +# if defined(_M_I86) +# define ARCHITECTURE_ID "I86" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#else +# define ARCHITECTURE_ID +#endif + +/* Convert integer to decimal digit literals. */ +#define DEC(n) \ + ('0' + (((n) / 10000000)%10)), \ + ('0' + (((n) / 1000000)%10)), \ + ('0' + (((n) / 100000)%10)), \ + ('0' + (((n) / 10000)%10)), \ + ('0' + (((n) / 1000)%10)), \ + ('0' + (((n) / 100)%10)), \ + ('0' + (((n) / 10)%10)), \ + ('0' + ((n) % 10)) + +/* Convert integer to hex digit literals. */ +#define HEX(n) \ + ('0' + ((n)>>28 & 0xF)), \ + ('0' + ((n)>>24 & 0xF)), \ + ('0' + ((n)>>20 & 0xF)), \ + ('0' + ((n)>>16 & 0xF)), \ + ('0' + ((n)>>12 & 0xF)), \ + ('0' + ((n)>>8 & 0xF)), \ + ('0' + ((n)>>4 & 0xF)), \ + ('0' + ((n) & 0xF)) + +/* Construct a string literal encoding the version number components. */ +#ifdef COMPILER_VERSION_MAJOR +char const info_version[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','[', + COMPILER_VERSION_MAJOR, +# ifdef COMPILER_VERSION_MINOR + '.', COMPILER_VERSION_MINOR, +# ifdef COMPILER_VERSION_PATCH + '.', COMPILER_VERSION_PATCH, +# ifdef COMPILER_VERSION_TWEAK + '.', COMPILER_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct a string literal encoding the version number components. */ +#ifdef SIMULATE_VERSION_MAJOR +char const info_simulate_version[] = { + 'I', 'N', 'F', 'O', ':', + 's','i','m','u','l','a','t','e','_','v','e','r','s','i','o','n','[', + SIMULATE_VERSION_MAJOR, +# ifdef SIMULATE_VERSION_MINOR + '.', SIMULATE_VERSION_MINOR, +# ifdef SIMULATE_VERSION_PATCH + '.', SIMULATE_VERSION_PATCH, +# ifdef SIMULATE_VERSION_TWEAK + '.', SIMULATE_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_platform = "INFO" ":" "platform[" PLATFORM_ID "]"; +char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; + + + + +#if !defined(__STDC__) +# if defined(_MSC_VER) && !defined(__clang__) +# define C_DIALECT "90" +# else +# define C_DIALECT +# endif +#elif __STDC_VERSION__ >= 201000L +# define C_DIALECT "11" +#elif __STDC_VERSION__ >= 199901L +# define C_DIALECT "99" +#else +# define C_DIALECT "90" +#endif +const char* info_language_dialect_default = + "INFO" ":" "dialect_default[" C_DIALECT "]"; + +/*--------------------------------------------------------------------------*/ + +#ifdef ID_VOID_MAIN +void main() {} +#else +# if defined(__CLASSIC_C__) +int main(argc, argv) int argc; char *argv[]; +# else +int main(int argc, char* argv[]) +# endif +{ + int require = 0; + require += info_compiler[argc]; + require += info_platform[argc]; + require += info_arch[argc]; +#ifdef COMPILER_VERSION_MAJOR + require += info_version[argc]; +#endif +#ifdef SIMULATE_ID + require += info_simulate[argc]; +#endif +#ifdef SIMULATE_VERSION_MAJOR + require += info_simulate_version[argc]; +#endif +#if defined(__CRAYXE) || defined(__CRAYXC) + require += info_cray[argc]; +#endif + require += info_language_dialect_default[argc]; + (void)argv; + return require; +} +#endif diff --git a/kk/CMakeFiles/3.8.2/CompilerIdCXX/CMakeCXXCompilerId.cpp b/kk/CMakeFiles/3.8.2/CompilerIdCXX/CMakeCXXCompilerId.cpp new file mode 100644 index 0000000..e7037e5 --- /dev/null +++ b/kk/CMakeFiles/3.8.2/CompilerIdCXX/CMakeCXXCompilerId.cpp @@ -0,0 +1,539 @@ +/* This source file must have a .cpp extension so that all C++ compilers + recognize the extension without flags. Borland does not know .cxx for + example. */ +#ifndef __cplusplus +# error "A C compiler has been selected for C++." +#endif + + +/* Version number components: V=Version, R=Revision, P=Patch + Version date components: YYYY=Year, MM=Month, DD=Day */ + +#if defined(__COMO__) +# define COMPILER_ID "Comeau" + /* __COMO_VERSION__ = VRR */ +# define COMPILER_VERSION_MAJOR DEC(__COMO_VERSION__ / 100) +# define COMPILER_VERSION_MINOR DEC(__COMO_VERSION__ % 100) + +#elif defined(__INTEL_COMPILER) || defined(__ICC) +# define COMPILER_ID "Intel" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif + /* __INTEL_COMPILER = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER/100) +# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER/10 % 10) +# if defined(__INTEL_COMPILER_UPDATE) +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER_UPDATE) +# else +# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER % 10) +# endif +# if defined(__INTEL_COMPILER_BUILD_DATE) + /* __INTEL_COMPILER_BUILD_DATE = YYYYMMDD */ +# define COMPILER_VERSION_TWEAK DEC(__INTEL_COMPILER_BUILD_DATE) +# endif +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif + +#elif defined(__PATHCC__) +# define COMPILER_ID "PathScale" +# define COMPILER_VERSION_MAJOR DEC(__PATHCC__) +# define COMPILER_VERSION_MINOR DEC(__PATHCC_MINOR__) +# if defined(__PATHCC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PATHCC_PATCHLEVEL__) +# endif + +#elif defined(__BORLANDC__) && defined(__CODEGEARC_VERSION__) +# define COMPILER_ID "Embarcadero" +# define COMPILER_VERSION_MAJOR HEX(__CODEGEARC_VERSION__>>24 & 0x00FF) +# define COMPILER_VERSION_MINOR HEX(__CODEGEARC_VERSION__>>16 & 0x00FF) +# define COMPILER_VERSION_PATCH DEC(__CODEGEARC_VERSION__ & 0xFFFF) + +#elif defined(__BORLANDC__) +# define COMPILER_ID "Borland" + /* __BORLANDC__ = 0xVRR */ +# define COMPILER_VERSION_MAJOR HEX(__BORLANDC__>>8) +# define COMPILER_VERSION_MINOR HEX(__BORLANDC__ & 0xFF) + +#elif defined(__WATCOMC__) && __WATCOMC__ < 1200 +# define COMPILER_ID "Watcom" + /* __WATCOMC__ = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(__WATCOMC__ / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__WATCOMC__) +# define COMPILER_ID "OpenWatcom" + /* __WATCOMC__ = VVRP + 1100 */ +# define COMPILER_VERSION_MAJOR DEC((__WATCOMC__ - 1100) / 100) +# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10) +# if (__WATCOMC__ % 10) > 0 +# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10) +# endif + +#elif defined(__SUNPRO_CC) +# define COMPILER_ID "SunPro" +# if __SUNPRO_CC >= 0x5100 + /* __SUNPRO_CC = 0xVRRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>12) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF) +# else + /* __SUNPRO_CC = 0xVRP */ +# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>8) +# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xF) +# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF) +# endif + +#elif defined(__HP_aCC) +# define COMPILER_ID "HP" + /* __HP_aCC = VVRRPP */ +# define COMPILER_VERSION_MAJOR DEC(__HP_aCC/10000) +# define COMPILER_VERSION_MINOR DEC(__HP_aCC/100 % 100) +# define COMPILER_VERSION_PATCH DEC(__HP_aCC % 100) + +#elif defined(__DECCXX) +# define COMPILER_ID "Compaq" + /* __DECCXX_VER = VVRRTPPPP */ +# define COMPILER_VERSION_MAJOR DEC(__DECCXX_VER/10000000) +# define COMPILER_VERSION_MINOR DEC(__DECCXX_VER/100000 % 100) +# define COMPILER_VERSION_PATCH DEC(__DECCXX_VER % 10000) + +#elif defined(__IBMCPP__) && defined(__COMPILER_VER__) +# define COMPILER_ID "zOS" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ >= 800 +# define COMPILER_ID "XL" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ < 800 +# define COMPILER_ID "VisualAge" + /* __IBMCPP__ = VRP */ +# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100) +# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10) +# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10) + +#elif defined(__PGI) +# define COMPILER_ID "PGI" +# define COMPILER_VERSION_MAJOR DEC(__PGIC__) +# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__) +# if defined(__PGIC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__) +# endif + +#elif defined(_CRAYC) +# define COMPILER_ID "Cray" +# define COMPILER_VERSION_MAJOR DEC(_RELEASE_MAJOR) +# define COMPILER_VERSION_MINOR DEC(_RELEASE_MINOR) + +#elif defined(__TI_COMPILER_VERSION__) +# define COMPILER_ID "TI" + /* __TI_COMPILER_VERSION__ = VVVRRRPPP */ +# define COMPILER_VERSION_MAJOR DEC(__TI_COMPILER_VERSION__/1000000) +# define COMPILER_VERSION_MINOR DEC(__TI_COMPILER_VERSION__/1000 % 1000) +# define COMPILER_VERSION_PATCH DEC(__TI_COMPILER_VERSION__ % 1000) + +#elif defined(__FUJITSU) || defined(__FCC_VERSION) || defined(__fcc_version) +# define COMPILER_ID "Fujitsu" + +#elif defined(__SCO_VERSION__) +# define COMPILER_ID "SCO" + +#elif defined(__clang__) && defined(__apple_build_version__) +# define COMPILER_ID "AppleClang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif +# define COMPILER_VERSION_TWEAK DEC(__apple_build_version__) + +#elif defined(__clang__) +# define COMPILER_ID "Clang" +# if defined(_MSC_VER) +# define SIMULATE_ID "MSVC" +# endif +# define COMPILER_VERSION_MAJOR DEC(__clang_major__) +# define COMPILER_VERSION_MINOR DEC(__clang_minor__) +# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__) +# if defined(_MSC_VER) + /* _MSC_VER = VVRR */ +# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100) +# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100) +# endif + +#elif defined(__GNUC__) || defined(__GNUG__) +# define COMPILER_ID "GNU" +# if defined(__GNUC__) +# define COMPILER_VERSION_MAJOR DEC(__GNUC__) +# else +# define COMPILER_VERSION_MAJOR DEC(__GNUG__) +# endif +# if defined(__GNUC_MINOR__) +# define COMPILER_VERSION_MINOR DEC(__GNUC_MINOR__) +# endif +# if defined(__GNUC_PATCHLEVEL__) +# define COMPILER_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__) +# endif + +#elif defined(_MSC_VER) +# define COMPILER_ID "MSVC" + /* _MSC_VER = VVRR */ +# define COMPILER_VERSION_MAJOR DEC(_MSC_VER / 100) +# define COMPILER_VERSION_MINOR DEC(_MSC_VER % 100) +# if defined(_MSC_FULL_VER) +# if _MSC_VER >= 1400 + /* _MSC_FULL_VER = VVRRPPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 100000) +# else + /* _MSC_FULL_VER = VVRRPPPP */ +# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 10000) +# endif +# endif +# if defined(_MSC_BUILD) +# define COMPILER_VERSION_TWEAK DEC(_MSC_BUILD) +# endif + +#elif defined(__VISUALDSPVERSION__) || defined(__ADSPBLACKFIN__) || defined(__ADSPTS__) || defined(__ADSP21000__) +# define COMPILER_ID "ADSP" +#if defined(__VISUALDSPVERSION__) + /* __VISUALDSPVERSION__ = 0xVVRRPP00 */ +# define COMPILER_VERSION_MAJOR HEX(__VISUALDSPVERSION__>>24) +# define COMPILER_VERSION_MINOR HEX(__VISUALDSPVERSION__>>16 & 0xFF) +# define COMPILER_VERSION_PATCH HEX(__VISUALDSPVERSION__>>8 & 0xFF) +#endif + +#elif defined(__IAR_SYSTEMS_ICC__ ) || defined(__IAR_SYSTEMS_ICC) +# define COMPILER_ID "IAR" + +#elif defined(__ARMCC_VERSION) +# define COMPILER_ID "ARMCC" +#if __ARMCC_VERSION >= 1000000 + /* __ARMCC_VERSION = VRRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/1000000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 100) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#else + /* __ARMCC_VERSION = VRPPPP */ + # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/100000) + # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 10) + # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000) +#endif + + +#elif defined(_SGI_COMPILER_VERSION) || defined(_COMPILER_VERSION) +# define COMPILER_ID "MIPSpro" +# if defined(_SGI_COMPILER_VERSION) + /* _SGI_COMPILER_VERSION = VRP */ +# define COMPILER_VERSION_MAJOR DEC(_SGI_COMPILER_VERSION/100) +# define COMPILER_VERSION_MINOR DEC(_SGI_COMPILER_VERSION/10 % 10) +# define COMPILER_VERSION_PATCH DEC(_SGI_COMPILER_VERSION % 10) +# else + /* _COMPILER_VERSION = VRP */ +# define COMPILER_VERSION_MAJOR DEC(_COMPILER_VERSION/100) +# define COMPILER_VERSION_MINOR DEC(_COMPILER_VERSION/10 % 10) +# define COMPILER_VERSION_PATCH DEC(_COMPILER_VERSION % 10) +# endif + + +/* These compilers are either not known or too old to define an + identification macro. Try to identify the platform and guess that + it is the native compiler. */ +#elif defined(__sgi) +# define COMPILER_ID "MIPSpro" + +#elif defined(__hpux) || defined(__hpua) +# define COMPILER_ID "HP" + +#else /* unknown compiler */ +# define COMPILER_ID "" +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_compiler = "INFO" ":" "compiler[" COMPILER_ID "]"; +#ifdef SIMULATE_ID +char const* info_simulate = "INFO" ":" "simulate[" SIMULATE_ID "]"; +#endif + +#ifdef __QNXNTO__ +char const* qnxnto = "INFO" ":" "qnxnto[]"; +#endif + +#if defined(__CRAYXE) || defined(__CRAYXC) +char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; +#endif + +#define STRINGIFY_HELPER(X) #X +#define STRINGIFY(X) STRINGIFY_HELPER(X) + +/* Identify known platforms by name. */ +#if defined(__linux) || defined(__linux__) || defined(linux) +# define PLATFORM_ID "Linux" + +#elif defined(__CYGWIN__) +# define PLATFORM_ID "Cygwin" + +#elif defined(__MINGW32__) +# define PLATFORM_ID "MinGW" + +#elif defined(__APPLE__) +# define PLATFORM_ID "Darwin" + +#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32) +# define PLATFORM_ID "Windows" + +#elif defined(__FreeBSD__) || defined(__FreeBSD) +# define PLATFORM_ID "FreeBSD" + +#elif defined(__NetBSD__) || defined(__NetBSD) +# define PLATFORM_ID "NetBSD" + +#elif defined(__OpenBSD__) || defined(__OPENBSD) +# define PLATFORM_ID "OpenBSD" + +#elif defined(__sun) || defined(sun) +# define PLATFORM_ID "SunOS" + +#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__) +# define PLATFORM_ID "AIX" + +#elif defined(__sgi) || defined(__sgi__) || defined(_SGI) +# define PLATFORM_ID "IRIX" + +#elif defined(__hpux) || defined(__hpux__) +# define PLATFORM_ID "HP-UX" + +#elif defined(__HAIKU__) +# define PLATFORM_ID "Haiku" + +#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS) +# define PLATFORM_ID "BeOS" + +#elif defined(__QNX__) || defined(__QNXNTO__) +# define PLATFORM_ID "QNX" + +#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__) +# define PLATFORM_ID "Tru64" + +#elif defined(__riscos) || defined(__riscos__) +# define PLATFORM_ID "RISCos" + +#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__) +# define PLATFORM_ID "SINIX" + +#elif defined(__UNIX_SV__) +# define PLATFORM_ID "UNIX_SV" + +#elif defined(__bsdos__) +# define PLATFORM_ID "BSDOS" + +#elif defined(_MPRAS) || defined(MPRAS) +# define PLATFORM_ID "MP-RAS" + +#elif defined(__osf) || defined(__osf__) +# define PLATFORM_ID "OSF1" + +#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv) +# define PLATFORM_ID "SCO_SV" + +#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX) +# define PLATFORM_ID "ULTRIX" + +#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX) +# define PLATFORM_ID "Xenix" + +#elif defined(__WATCOMC__) +# if defined(__LINUX__) +# define PLATFORM_ID "Linux" + +# elif defined(__DOS__) +# define PLATFORM_ID "DOS" + +# elif defined(__OS2__) +# define PLATFORM_ID "OS2" + +# elif defined(__WINDOWS__) +# define PLATFORM_ID "Windows3x" + +# else /* unknown platform */ +# define PLATFORM_ID +# endif + +#else /* unknown platform */ +# define PLATFORM_ID + +#endif + +/* For windows compilers MSVC and Intel we can determine + the architecture of the compiler being used. This is because + the compilers do not have flags that can change the architecture, + but rather depend on which compiler is being used +*/ +#if defined(_WIN32) && defined(_MSC_VER) +# if defined(_M_IA64) +# define ARCHITECTURE_ID "IA64" + +# elif defined(_M_X64) || defined(_M_AMD64) +# define ARCHITECTURE_ID "x64" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# elif defined(_M_ARM) +# if _M_ARM == 4 +# define ARCHITECTURE_ID "ARMV4I" +# elif _M_ARM == 5 +# define ARCHITECTURE_ID "ARMV5I" +# else +# define ARCHITECTURE_ID "ARMV" STRINGIFY(_M_ARM) +# endif + +# elif defined(_M_MIPS) +# define ARCHITECTURE_ID "MIPS" + +# elif defined(_M_SH) +# define ARCHITECTURE_ID "SHx" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#elif defined(__WATCOMC__) +# if defined(_M_I86) +# define ARCHITECTURE_ID "I86" + +# elif defined(_M_IX86) +# define ARCHITECTURE_ID "X86" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + +#else +# define ARCHITECTURE_ID +#endif + +/* Convert integer to decimal digit literals. */ +#define DEC(n) \ + ('0' + (((n) / 10000000)%10)), \ + ('0' + (((n) / 1000000)%10)), \ + ('0' + (((n) / 100000)%10)), \ + ('0' + (((n) / 10000)%10)), \ + ('0' + (((n) / 1000)%10)), \ + ('0' + (((n) / 100)%10)), \ + ('0' + (((n) / 10)%10)), \ + ('0' + ((n) % 10)) + +/* Convert integer to hex digit literals. */ +#define HEX(n) \ + ('0' + ((n)>>28 & 0xF)), \ + ('0' + ((n)>>24 & 0xF)), \ + ('0' + ((n)>>20 & 0xF)), \ + ('0' + ((n)>>16 & 0xF)), \ + ('0' + ((n)>>12 & 0xF)), \ + ('0' + ((n)>>8 & 0xF)), \ + ('0' + ((n)>>4 & 0xF)), \ + ('0' + ((n) & 0xF)) + +/* Construct a string literal encoding the version number components. */ +#ifdef COMPILER_VERSION_MAJOR +char const info_version[] = { + 'I', 'N', 'F', 'O', ':', + 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','[', + COMPILER_VERSION_MAJOR, +# ifdef COMPILER_VERSION_MINOR + '.', COMPILER_VERSION_MINOR, +# ifdef COMPILER_VERSION_PATCH + '.', COMPILER_VERSION_PATCH, +# ifdef COMPILER_VERSION_TWEAK + '.', COMPILER_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct a string literal encoding the version number components. */ +#ifdef SIMULATE_VERSION_MAJOR +char const info_simulate_version[] = { + 'I', 'N', 'F', 'O', ':', + 's','i','m','u','l','a','t','e','_','v','e','r','s','i','o','n','[', + SIMULATE_VERSION_MAJOR, +# ifdef SIMULATE_VERSION_MINOR + '.', SIMULATE_VERSION_MINOR, +# ifdef SIMULATE_VERSION_PATCH + '.', SIMULATE_VERSION_PATCH, +# ifdef SIMULATE_VERSION_TWEAK + '.', SIMULATE_VERSION_TWEAK, +# endif +# endif +# endif + ']','\0'}; +#endif + +/* Construct the string literal in pieces to prevent the source from + getting matched. Store it in a pointer rather than an array + because some compilers will just produce instructions to fill the + array rather than assigning a pointer to a static array. */ +char const* info_platform = "INFO" ":" "platform[" PLATFORM_ID "]"; +char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; + + + + +const char* info_language_dialect_default = "INFO" ":" "dialect_default[" +#if __cplusplus > 201402L + "17" +#elif __cplusplus >= 201402L + "14" +#elif __cplusplus >= 201103L + "11" +#else + "98" +#endif +"]"; + +/*--------------------------------------------------------------------------*/ + +int main(int argc, char* argv[]) +{ + int require = 0; + require += info_compiler[argc]; + require += info_platform[argc]; +#ifdef COMPILER_VERSION_MAJOR + require += info_version[argc]; +#endif +#ifdef SIMULATE_ID + require += info_simulate[argc]; +#endif +#ifdef SIMULATE_VERSION_MAJOR + require += info_simulate_version[argc]; +#endif +#if defined(__CRAYXE) || defined(__CRAYXC) + require += info_cray[argc]; +#endif + require += info_language_dialect_default[argc]; + (void)argv; + return require; +} diff --git a/kk/CMakeFiles/CMakeDirectoryInformation.cmake b/kk/CMakeFiles/CMakeDirectoryInformation.cmake new file mode 100644 index 0000000..4a0af0d --- /dev/null +++ b/kk/CMakeFiles/CMakeDirectoryInformation.cmake @@ -0,0 +1,16 @@ +# CMAKE generated file: DO NOT EDIT! +# Generated by "Unix Makefiles" Generator, CMake Version 3.8 + +# Relative path conversion top directories. +set(CMAKE_RELATIVE_PATH_TOP_SOURCE "/Users/tchen/Documents/acnotes/kk") +set(CMAKE_RELATIVE_PATH_TOP_BINARY "/Users/tchen/Documents/acnotes/kk") + +# Force unix paths in dependencies. +set(CMAKE_FORCE_UNIX_PATHS 1) + + +# The C and CXX include file regular expressions for this directory. +set(CMAKE_C_INCLUDE_REGEX_SCAN "^.*$") +set(CMAKE_C_INCLUDE_REGEX_COMPLAIN "^$") +set(CMAKE_CXX_INCLUDE_REGEX_SCAN ${CMAKE_C_INCLUDE_REGEX_SCAN}) +set(CMAKE_CXX_INCLUDE_REGEX_COMPLAIN 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option 'fopenmp=' +make[1]: *** [CMakeFiles/cmTC_68ba6.dir/src.c.o] Error 1 +make: *** [cmTC_68ba6/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_0b55f/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_0b55f.dir/build.make CMakeFiles/cmTC_0b55f.dir/build +Building C object CMakeFiles/cmTC_0b55f.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_0b55f.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_0b55f.dir/src.c.o] Error 1 +make: *** [cmTC_0b55f/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_00b56/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_00b56.dir/build.make CMakeFiles/cmTC_00b56.dir/build +Building C object CMakeFiles/cmTC_00b56.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_00b56.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unsupported option '-fopenmp' +make[1]: *** [CMakeFiles/cmTC_00b56.dir/src.c.o] Error 1 +make: *** [cmTC_00b56/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_92a66/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_92a66.dir/build.make CMakeFiles/cmTC_92a66.dir/build +Building C object CMakeFiles/cmTC_92a66.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_92a66.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: no such file or directory: '/openmp' +make[1]: *** [CMakeFiles/cmTC_92a66.dir/src.c.o] Error 1 +make: *** [cmTC_92a66/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_6a70d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_6a70d.dir/build.make CMakeFiles/cmTC_6a70d.dir/build +Building C object CMakeFiles/cmTC_6a70d.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_6a70d.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-Qopenmp' +make[1]: *** [CMakeFiles/cmTC_6a70d.dir/src.c.o] Error 1 +make: *** [cmTC_6a70d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_f9d19/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_f9d19.dir/build.make CMakeFiles/cmTC_f9d19.dir/build +Building C object CMakeFiles/cmTC_f9d19.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_f9d19.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_f9d19.dir/src.c.o] Error 1 +make: *** [cmTC_f9d19/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_03c0b/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_03c0b.dir/build.make CMakeFiles/cmTC_03c0b.dir/build +Building C object CMakeFiles/cmTC_03c0b.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_03c0b.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c: 'linker' input unused +make[1]: *** [CMakeFiles/cmTC_03c0b.dir/src.c.o] Error 1 +make: *** [cmTC_03c0b/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_ef9ea/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_ef9ea.dir/build.make CMakeFiles/cmTC_ef9ea.dir/build +Building C object CMakeFiles/cmTC_ef9ea.dir/src.c.o 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CMakeFiles/cmTC_698d5.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_698d5.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_698d5.dir/src.cxx.o] Error 1 +make: *** [cmTC_698d5/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_48cae/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_48cae.dir/build.make CMakeFiles/cmTC_48cae.dir/build +Building CXX object CMakeFiles/cmTC_48cae.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_48cae.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unsupported option '-fopenmp' +make[1]: *** [CMakeFiles/cmTC_48cae.dir/src.cxx.o] Error 1 +make: *** [cmTC_48cae/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_274cf/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_274cf.dir/build.make CMakeFiles/cmTC_274cf.dir/build +Building CXX object CMakeFiles/cmTC_274cf.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_274cf.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: no such file or directory: '/openmp' +make[1]: *** [CMakeFiles/cmTC_274cf.dir/src.cxx.o] Error 1 +make: *** [cmTC_274cf/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_3dfca/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_3dfca.dir/build.make CMakeFiles/cmTC_3dfca.dir/build +Building CXX object CMakeFiles/cmTC_3dfca.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_3dfca.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-Qopenmp' +make[1]: *** [CMakeFiles/cmTC_3dfca.dir/src.cxx.o] Error 1 +make: *** [cmTC_3dfca/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_ac9e0/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_ac9e0.dir/build.make CMakeFiles/cmTC_ac9e0.dir/build +Building CXX object CMakeFiles/cmTC_ac9e0.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_ac9e0.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_ac9e0.dir/src.cxx.o] Error 1 +make: *** [cmTC_ac9e0/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_312c5/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_312c5.dir/build.make CMakeFiles/cmTC_312c5.dir/build +Building CXX object CMakeFiles/cmTC_312c5.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_312c5.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx: 'linker' input unused +make[1]: *** [CMakeFiles/cmTC_312c5.dir/src.cxx.o] Error 1 +make: *** [cmTC_312c5/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_a875c/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_a875c.dir/build.make CMakeFiles/cmTC_a875c.dir/build +Building CXX object CMakeFiles/cmTC_a875c.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED +Oopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_a875c.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: no such file or directory: '+Oopenmp' +make[1]: *** [CMakeFiles/cmTC_a875c.dir/src.cxx.o] Error 1 +make: *** [cmTC_a875c/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_49c33/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_49c33.dir/build.make CMakeFiles/cmTC_49c33.dir/build +Building CXX object CMakeFiles/cmTC_49c33.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -qsmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_49c33.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-qsmp' +make[1]: *** [CMakeFiles/cmTC_49c33.dir/src.cxx.o] Error 1 +make: *** [cmTC_49c33/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_4d9d6/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_4d9d6.dir/build.make CMakeFiles/cmTC_4d9d6.dir/build +Building CXX object CMakeFiles/cmTC_4d9d6.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -mp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_4d9d6.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-mp' +make[1]: *** [CMakeFiles/cmTC_4d9d6.dir/src.cxx.o] Error 1 +make: *** [cmTC_4d9d6/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_a2a9d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_a2a9d.dir/build.make CMakeFiles/cmTC_a2a9d.dir/build +Building C object CMakeFiles/cmTC_a2a9d.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -fopenmp=libomp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_a2a9d.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unsupported argument 'libomp' to option 'fopenmp=' +make[1]: *** [CMakeFiles/cmTC_a2a9d.dir/src.c.o] Error 1 +make: *** [cmTC_a2a9d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_5b1e4/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_5b1e4.dir/build.make CMakeFiles/cmTC_5b1e4.dir/build +Building C object CMakeFiles/cmTC_5b1e4.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_5b1e4.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_5b1e4.dir/src.c.o] Error 1 +make: *** [cmTC_5b1e4/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_4a626/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_4a626.dir/build.make CMakeFiles/cmTC_4a626.dir/build +Building C object CMakeFiles/cmTC_4a626.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_4a626.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unsupported option '-fopenmp' +make[1]: *** [CMakeFiles/cmTC_4a626.dir/src.c.o] Error 1 +make: *** [cmTC_4a626/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_ed328/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_ed328.dir/build.make CMakeFiles/cmTC_ed328.dir/build +Building C object CMakeFiles/cmTC_ed328.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_ed328.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: no such file or directory: '/openmp' +make[1]: *** [CMakeFiles/cmTC_ed328.dir/src.c.o] Error 1 +make: *** [cmTC_ed328/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_fe8fa/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_fe8fa.dir/build.make CMakeFiles/cmTC_fe8fa.dir/build +Building C object CMakeFiles/cmTC_fe8fa.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_fe8fa.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-Qopenmp' +make[1]: *** [CMakeFiles/cmTC_fe8fa.dir/src.c.o] Error 1 +make: *** [cmTC_fe8fa/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_7cd36/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_7cd36.dir/build.make CMakeFiles/cmTC_7cd36.dir/build +Building C object CMakeFiles/cmTC_7cd36.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_7cd36.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_7cd36.dir/src.c.o] Error 1 +make: *** [cmTC_7cd36/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_eed0d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_eed0d.dir/build.make CMakeFiles/cmTC_eed0d.dir/build +Building C object CMakeFiles/cmTC_eed0d.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_eed0d.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c: 'linker' input unused +make[1]: *** [CMakeFiles/cmTC_eed0d.dir/src.c.o] Error 1 +make: *** [cmTC_eed0d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_7d749/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_7d749.dir/build.make CMakeFiles/cmTC_7d749.dir/build +Building C object CMakeFiles/cmTC_7d749.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED +Oopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_7d749.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: no such file or directory: '+Oopenmp' +make[1]: *** [CMakeFiles/cmTC_7d749.dir/src.c.o] Error 1 +make: *** [cmTC_7d749/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_257a9/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_257a9.dir/build.make CMakeFiles/cmTC_257a9.dir/build +Building C object CMakeFiles/cmTC_257a9.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -qsmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_257a9.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-qsmp' +make[1]: *** [CMakeFiles/cmTC_257a9.dir/src.c.o] Error 1 +make: *** [cmTC_257a9/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_f196b/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_f196b.dir/build.make CMakeFiles/cmTC_f196b.dir/build +Building C object CMakeFiles/cmTC_f196b.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -mp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_f196b.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-mp' +make[1]: *** [CMakeFiles/cmTC_f196b.dir/src.c.o] Error 1 +make: *** [cmTC_f196b/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_e1a14/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_e1a14.dir/build.make CMakeFiles/cmTC_e1a14.dir/build +Building CXX object CMakeFiles/cmTC_e1a14.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -fopenmp=libomp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_e1a14.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unsupported argument 'libomp' to option 'fopenmp=' +make[1]: *** [CMakeFiles/cmTC_e1a14.dir/src.cxx.o] Error 1 +make: *** [cmTC_e1a14/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_577cd/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_577cd.dir/build.make CMakeFiles/cmTC_577cd.dir/build +Building CXX object CMakeFiles/cmTC_577cd.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_577cd.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_577cd.dir/src.cxx.o] Error 1 +make: *** [cmTC_577cd/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_1de22/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_1de22.dir/build.make CMakeFiles/cmTC_1de22.dir/build +Building CXX object CMakeFiles/cmTC_1de22.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_1de22.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unsupported option '-fopenmp' +make[1]: *** [CMakeFiles/cmTC_1de22.dir/src.cxx.o] Error 1 +make: *** [cmTC_1de22/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_ead5d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_ead5d.dir/build.make CMakeFiles/cmTC_ead5d.dir/build +Building CXX object CMakeFiles/cmTC_ead5d.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_ead5d.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: no such file or directory: '/openmp' +make[1]: *** [CMakeFiles/cmTC_ead5d.dir/src.cxx.o] Error 1 +make: *** [cmTC_ead5d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_eacd2/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_eacd2.dir/build.make CMakeFiles/cmTC_eacd2.dir/build +Building CXX object CMakeFiles/cmTC_eacd2.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_eacd2.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-Qopenmp' +make[1]: *** [CMakeFiles/cmTC_eacd2.dir/src.cxx.o] Error 1 +make: *** [cmTC_eacd2/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_b8639/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_b8639.dir/build.make CMakeFiles/cmTC_b8639.dir/build +Building CXX object CMakeFiles/cmTC_b8639.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_b8639.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[1]: *** [CMakeFiles/cmTC_b8639.dir/src.cxx.o] Error 1 +make: *** [cmTC_b8639/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_5486b/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_5486b.dir/build.make CMakeFiles/cmTC_5486b.dir/build +Building CXX object CMakeFiles/cmTC_5486b.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_5486b.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx: 'linker' input unused +make[1]: *** [CMakeFiles/cmTC_5486b.dir/src.cxx.o] Error 1 +make: *** [cmTC_5486b/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_aa02b/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_aa02b.dir/build.make CMakeFiles/cmTC_aa02b.dir/build +Building CXX object CMakeFiles/cmTC_aa02b.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED +Oopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_aa02b.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: no such file or directory: '+Oopenmp' +make[1]: *** [CMakeFiles/cmTC_aa02b.dir/src.cxx.o] Error 1 +make: *** [cmTC_aa02b/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_2ddd6/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_2ddd6.dir/build.make CMakeFiles/cmTC_2ddd6.dir/build +Building CXX object CMakeFiles/cmTC_2ddd6.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -qsmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_2ddd6.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-qsmp' +make[1]: *** [CMakeFiles/cmTC_2ddd6.dir/src.cxx.o] Error 1 +make: *** [cmTC_2ddd6/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_c3d15/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_c3d15.dir/build.make CMakeFiles/cmTC_c3d15.dir/build +Building CXX object CMakeFiles/cmTC_c3d15.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -mp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_c3d15.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-mp' +make[1]: *** [CMakeFiles/cmTC_c3d15.dir/src.cxx.o] Error 1 +make: *** [cmTC_c3d15/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_f05b5/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_f05b5.dir/build.make CMakeFiles/cmTC_f05b5.dir/build +Building C object CMakeFiles/cmTC_f05b5.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -fopenmp=libomp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_f05b5.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unsupported argument 'libomp' to option 'fopenmp=' +make[2]: *** [CMakeFiles/cmTC_f05b5.dir/src.c.o] Error 1 +make[1]: *** [cmTC_f05b5/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_4d7c1/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_4d7c1.dir/build.make CMakeFiles/cmTC_4d7c1.dir/build +Building C object CMakeFiles/cmTC_4d7c1.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_4d7c1.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[2]: *** [CMakeFiles/cmTC_4d7c1.dir/src.c.o] Error 1 +make[1]: *** [cmTC_4d7c1/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_0273d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_0273d.dir/build.make CMakeFiles/cmTC_0273d.dir/build +Building C object CMakeFiles/cmTC_0273d.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_0273d.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unsupported option '-fopenmp' +make[2]: *** [CMakeFiles/cmTC_0273d.dir/src.c.o] Error 1 +make[1]: *** [cmTC_0273d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_0fc3e/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_0fc3e.dir/build.make CMakeFiles/cmTC_0fc3e.dir/build +Building C object CMakeFiles/cmTC_0fc3e.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_0fc3e.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: no such file or directory: '/openmp' +make[2]: *** [CMakeFiles/cmTC_0fc3e.dir/src.c.o] Error 1 +make[1]: *** [cmTC_0fc3e/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_9de5d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_9de5d.dir/build.make CMakeFiles/cmTC_9de5d.dir/build +Building C object CMakeFiles/cmTC_9de5d.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_9de5d.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-Qopenmp' +make[2]: *** [CMakeFiles/cmTC_9de5d.dir/src.c.o] Error 1 +make[1]: *** [cmTC_9de5d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_9b97e/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_9b97e.dir/build.make CMakeFiles/cmTC_9b97e.dir/build +Building C object CMakeFiles/cmTC_9b97e.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_9b97e.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[2]: *** [CMakeFiles/cmTC_9b97e.dir/src.c.o] Error 1 +make[1]: *** [cmTC_9b97e/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_09dd2/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_09dd2.dir/build.make CMakeFiles/cmTC_09dd2.dir/build +Building C object CMakeFiles/cmTC_09dd2.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_09dd2.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c: 'linker' input unused +make[2]: *** [CMakeFiles/cmTC_09dd2.dir/src.c.o] Error 1 +make[1]: *** [cmTC_09dd2/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_76a21/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_76a21.dir/build.make CMakeFiles/cmTC_76a21.dir/build +Building C object CMakeFiles/cmTC_76a21.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED +Oopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_76a21.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: no such file or directory: '+Oopenmp' +make[2]: *** [CMakeFiles/cmTC_76a21.dir/src.c.o] Error 1 +make[1]: *** [cmTC_76a21/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_08302/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_08302.dir/build.make CMakeFiles/cmTC_08302.dir/build +Building C object CMakeFiles/cmTC_08302.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -qsmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_08302.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-qsmp' +make[2]: *** [CMakeFiles/cmTC_08302.dir/src.c.o] Error 1 +make[1]: *** [cmTC_08302/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_70220/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_70220.dir/build.make CMakeFiles/cmTC_70220.dir/build +Building C object CMakeFiles/cmTC_70220.dir/src.c.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -DOpenMP_FLAG_DETECTED -mp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_70220.dir/src.c.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.c +clang: error: unknown argument: '-mp' +make[2]: *** [CMakeFiles/cmTC_70220.dir/src.c.o] Error 1 +make[1]: *** [cmTC_70220/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_3d10f/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_3d10f.dir/build.make CMakeFiles/cmTC_3d10f.dir/build +Building CXX object CMakeFiles/cmTC_3d10f.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -fopenmp=libomp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_3d10f.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unsupported argument 'libomp' to option 'fopenmp=' +make[2]: *** [CMakeFiles/cmTC_3d10f.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_3d10f/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_79725/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_79725.dir/build.make CMakeFiles/cmTC_79725.dir/build +Building CXX object CMakeFiles/cmTC_79725.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_79725.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[2]: *** [CMakeFiles/cmTC_79725.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_79725/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_bb3c4/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_bb3c4.dir/build.make CMakeFiles/cmTC_bb3c4.dir/build +Building CXX object CMakeFiles/cmTC_bb3c4.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -fopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_bb3c4.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unsupported option '-fopenmp' +make[2]: *** [CMakeFiles/cmTC_bb3c4.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_bb3c4/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_99f2d/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_99f2d.dir/build.make CMakeFiles/cmTC_99f2d.dir/build +Building CXX object CMakeFiles/cmTC_99f2d.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED /openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_99f2d.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: no such file or directory: '/openmp' +make[2]: *** [CMakeFiles/cmTC_99f2d.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_99f2d/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_dfb4e/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_dfb4e.dir/build.make CMakeFiles/cmTC_dfb4e.dir/build +Building CXX object CMakeFiles/cmTC_dfb4e.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -Qopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_dfb4e.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-Qopenmp' +make[2]: *** [CMakeFiles/cmTC_dfb4e.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_dfb4e/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_645b5/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_645b5.dir/build.make CMakeFiles/cmTC_645b5.dir/build +Building CXX object CMakeFiles/cmTC_645b5.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -openmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_645b5.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +/Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx:2:10: fatal error: 'omp.h' file not found +#include + ^ +1 error generated. +make[2]: *** [CMakeFiles/cmTC_645b5.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_645b5/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + +Performing C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_25937/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_25937.dir/build.make CMakeFiles/cmTC_25937.dir/build +Building CXX object CMakeFiles/cmTC_25937.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -xopenmp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_25937.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: language not recognized: 'openmp' +clang: warning: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx: 'linker' input unused +make[2]: *** [CMakeFiles/cmTC_25937.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_25937/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + 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C++ SOURCE FILE Test OpenMP_FLAG_DETECTED failed with the following output: +Change Dir: /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp + +Run Build Command:"/usr/bin/make" "cmTC_7cf4b/fast" +/Applications/Xcode.app/Contents/Developer/usr/bin/make -f CMakeFiles/cmTC_7cf4b.dir/build.make CMakeFiles/cmTC_7cf4b.dir/build +Building CXX object CMakeFiles/cmTC_7cf4b.dir/src.cxx.o +/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -DOpenMP_FLAG_DETECTED -mp -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk -o CMakeFiles/cmTC_7cf4b.dir/src.cxx.o -c /Users/tchen/Documents/acnotes/kk/CMakeFiles/CMakeTmp/src.cxx +clang: error: unknown argument: '-mp' +make[2]: *** [CMakeFiles/cmTC_7cf4b.dir/src.cxx.o] Error 1 +make[1]: *** [cmTC_7cf4b/fast] Error 2 + +Source file was: + +#include +int main() { +#ifdef _OPENMP + return 0; +#else + breaks_on_purpose +#endif +} + diff --git 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b/mbook/box/singularity/SpM.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = "BoxTime.dat" +DATASPACE =time +KERNEL =fermionic +NDAT =1001 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.0000001 diff --git a/mbook/box/singularity/SpMBoxData.nb b/mbook/box/singularity/SpMBoxData.nb new file mode 100644 index 0000000..b759809 --- /dev/null +++ b/mbook/box/singularity/SpMBoxData.nb @@ -0,0 +1,1190 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 11.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 58141, 1182] +NotebookOptionsPosition[ 56435, 1121] +NotebookOutlinePosition[ 56778, 1136] +CellTagsIndexPosition[ 56735, 1133] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Box 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a/mbook/krho-b50/l7/yprime_S.dat b/mbook/krho-b50/l7/yprime_S.dat new file mode 100644 index 0000000..fac5a5b --- /dev/null +++ b/mbook/krho-b50/l7/yprime_S.dat @@ -0,0 +1,28 @@ +2.93452 2.9346 -7.79166e-05 +-1.5184 -1.51855 0.000155174 +0.673136 0.673387 -0.00025093 +0.176093 0.176462 -0.00036889 +0.019493 0.0190153 0.000477686 +0.0154218 0.0148719 0.000549903 +0.00279076 0.00337039 -0.000579628 +0.00215682 0.00268209 -0.000525263 +-0.000359362 -0.000660625 0.000301263 +0.000214147 0.000128257 8.58908e-05 +0.000236156 -9.04851e-05 0.000326641 +0.000181837 5.21803e-05 0.000129657 +0.000135698 1.37751e-05 0.000121923 +0.000106321 -2.82015e-06 0.000109141 +8.49582e-05 5.06577e-08 8.49076e-05 +-6.86135e-05 -4.45115e-07 -6.81684e-05 +-5.60182e-05 1.02072e-08 -5.60284e-05 +-4.61891e-05 1.00853e-08 -4.61992e-05 +-3.84136e-05 -3.15312e-09 -3.84105e-05 +3.21913e-05 8.83164e-10 3.21904e-05 +-2.71617e-05 1.8657e-10 -2.71619e-05 +-2.30593e-05 -1.21099e-12 -2.30593e-05 +1.9686e-05 1.12434e-11 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and b/mbook/rho-b50/rho.png differ diff --git a/mbook/rho-b50/spec-r.fig b/mbook/rho-b50/spec-r.fig new file mode 100644 index 0000000..029fa29 Binary files /dev/null and b/mbook/rho-b50/spec-r.fig differ diff --git a/mbook/rho-b50/spec-r.png b/mbook/rho-b50/spec-r.png new file mode 100644 index 0000000..6ca47c9 Binary files /dev/null and b/mbook/rho-b50/spec-r.png differ diff --git a/mbook/rhoprime-b50/SpM.param b/mbook/rhoprime-b50/SpM.param new file mode 100644 index 0000000..eedafea --- /dev/null +++ b/mbook/rhoprime-b50/SpM.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = "TripleGaussianFrequency.dat" +DATASPACE =frequency +KERNEL =fermionic +NDAT =1000 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =0.0002 + +LAMBDA =0.000001 diff --git a/mbook/rhoprime-b50/TripleGaussianFrequency.dat b/mbook/rhoprime-b50/TripleGaussianFrequency.dat new file mode 100644 index 0000000..290e139 --- /dev/null +++ b/mbook/rhoprime-b50/TripleGaussianFrequency.dat @@ -0,0 +1,1000 @@ 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a/mbook/semicircle/singularity/l7-it7/yprime_S.dat b/mbook/semicircle/singularity/l7-it7/yprime_S.dat new file mode 100644 index 0000000..16dd205 --- /dev/null +++ b/mbook/semicircle/singularity/l7-it7/yprime_S.dat @@ -0,0 +1,55 @@ +0.631968 0.631984 -1.50266e-05 +6.52256e-16 -1.39783e-05 1.39783e-05 +1.0414 1.04127 0.00013734 +1.7486e-15 4.7145e-07 -4.7145e-07 +1.00949 1.00911 0.00037308 +4.996e-15 -1.72546e-05 1.72546e-05 +0.524225 0.523845 0.000379589 +3.83027e-15 1.22593e-05 -1.22593e-05 +0.0359485 0.0357889 0.000159676 +-2.16493e-15 -2.27415e-05 2.27415e-05 +0.0769172 0.0768308 8.63504e-05 +7.99361e-15 5.30329e-07 -5.30329e-07 +-0.0160802 -0.0158783 -0.000201912 +-5.70377e-15 6.36188e-06 -6.36188e-06 +0.00894971 0.00908006 -0.000130353 +1.09635e-15 -4.38857e-07 4.38857e-07 +-0.00276944 -0.00277052 1.08492e-06 +3.19189e-15 1.1603e-06 -1.1603e-06 +-0.000860731 -0.000910205 4.94745e-05 +-1.72085e-15 -4.42864e-08 4.42864e-08 +0.000283628 0.00033178 -4.81513e-05 +-1.01308e-15 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-7.29402e-22 -1.82137e-09 +4.2015e-11 -3.82385e-21 4.2015e-11 +1.80107e-09 -2.30609e-22 1.80107e-09 diff --git a/mbook/spec-b50/SpM.param b/mbook/spec-b50/SpM.param new file mode 100644 index 0000000..fa37be2 --- /dev/null +++ b/mbook/spec-b50/SpM.param @@ -0,0 +1,12 @@ +BETA = 50 +DATA = "TripleGaussianFrequency.dat" +DATASPACE =frequency +KERNEL =fermionic +NDAT =1000 +NORM =1 +NO_ERRORS=1 +PARTICLE_HOLE_SYMMETRY =1 +RHO arg =20 +RHOPRIME =200 + +LAMBDA =0.01 diff --git a/mbook/spec-b50/TripleGaussianFrequency.dat b/mbook/spec-b50/TripleGaussianFrequency.dat new file mode 100644 index 0000000..290e139 --- /dev/null +++ b/mbook/spec-b50/TripleGaussianFrequency.dat @@ -0,0 +1,1000 @@ +0.1884955592153876 -1.3348348393245837 +0.3141592653589793 -1.0775947561981254 +0.4398229715025711 -0.9294290772155577 +0.5654866776461628 -0.8301547150240809 +0.6911503837897546 -0.7564696037296741 +0.8168140899333463 -0.6979192146835289 +0.942477796076938 -0.6492460375385086 +1.0681415022205298 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-0,0 +1,12 @@ +{\rtf1\ansi\ansicpg1252\cocoartf1404\cocoasubrtf460 +{\fonttbl\f0\fnil\fcharset0 Menlo-Regular;} +{\colortbl;\red255\green255\blue255;} +\margl1440\margr1440\vieww10800\viewh8400\viewkind0 +\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\partightenfactor0 + +\f0\fs22 \cf0 \CocoaLigature0 constraint violations: z'-x': 7.22189e-18 s'-x: 4.87527e-18\ + norm: 2.22045e-16 positivity: 5.4824e-12\ + chi2 term: 3.70651e-05 l1 of x': 0.0885605\ + ns: 28\ + objective: 0.00092267\ +moving on.} \ No newline at end of file diff --git a/mbook/spec-b50/lam0.01-rhop200-it7/krho.dat b/mbook/spec-b50/lam0.01-rhop200-it7/krho.dat new file mode 100644 index 0000000..8999919 --- /dev/null +++ b/mbook/spec-b50/lam0.01-rhop200-it7/krho.dat @@ -0,0 +1,1000 @@ +-1.3348562110747 +-1.0782105469728 +-0.92671527029421 +-0.82968968620105 +-0.75803308955799 +-0.7003597899524 +-0.65170027151984 +-0.60954456630867 +-0.57243441983726 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b/mbook/test_selfenergy/spectrum_imsigma-pi.png new file mode 100644 index 0000000..87672a9 Binary files /dev/null and b/mbook/test_selfenergy/spectrum_imsigma-pi.png differ diff --git a/src/SpM_ADMM.cpp b/src/SpM_ADMM.cpp index 845f84e..2baa00e 100644 --- a/src/SpM_ADMM.cpp +++ b/src/SpM_ADMM.cpp @@ -101,6 +101,8 @@ void ADMM::print_info(std::ostream &os) const{ < #include //needed for Legendre transform namespace bmth = boost::math; +#include // We provide a file with data points and error bars, the latter are used only if // COVARIANCE_MATRIX is not set. The format is @@ -69,6 +70,12 @@ void KernelAndGridIO::read_data_from_text_file(const alps::params& p) { if(!no_errors_) sigma_[datIn] = dX_i / norm; datIn++; } + std::string filename1="y.dat"; + std::ofstream y_file(filename1); + y_file<(ndat_) diff --git a/test/SpMTest.cpp b/test/SpMTest.cpp index 71e6f39..1b52402 100644 --- a/test/SpMTest.cpp +++ b/test/SpMTest.cpp @@ -21,6 +21,9 @@ #include #include #include +#include +#include + double gaussian(double x){ //return gaussian(x,0,1,1); @@ -66,6 +69,18 @@ void matsubara_gf_to_param(alps::params &p, double beta, int nmax, double (*fun) } gsl_integration_workspace_free (w); } +void imag_time_gf_to_param(alps::params &p, int nmax, double beta){ + + //todo: put in the actual imaginary time green's function + for(int j=0;j norm(0., 0.00001); + for(int i=0;i<1001;++i){ + std::cout<0\,\,\forall j +\] + +\end_inset + +Note that the way the Maxent code was set up, +\begin_inset Formula $\mathcal{A}$ +\end_inset + + already contains a multiplication by a frequency element, such that the + spectral function at frequency index +\begin_inset Formula $k$ +\end_inset + + is given by +\begin_inset Formula $\mathcal{A}_{k}/\Delta\omega_{k}.$ +\end_inset + + The optimization problem is of the form of a constrained LASSO problem + with two constraints: a constraint that requires a convex optimization + (the positivity), and a constraint for the norm. + For more possible constraints see below. +\end_layout + +\begin_layout Section +Optimization without (physical) constraints +\end_layout + +\begin_layout Standard +The optimization of Eq. +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:objective" + +\end_inset + + without the physical constraints is fairly straightforward with ADMM: we + follow section 6.4, on LASSO, and minimize +\begin_inset Formula +\[ +L^{\lambda}(x')=\frac{{1}}{2}||Sx'-y'||_{2}^{2}+\lambda|x'|_{1} +\] + +\end_inset + +which we write as +\begin_inset Formula +\[ +\text{{minimize}\ \ }f(x')+g(z') +\] + +\end_inset + + +\begin_inset Formula +\[ +\text{{subject\ to}\ \ }x'-z'=0 +\] + +\end_inset + +where we define +\begin_inset Formula $f(x')=\frac{1}{2}||Sx'-y'||_{2}^{2}$ +\end_inset + + and +\begin_inset Formula $g(z')=\lambda|z'|_{1}$ +\end_inset + +. + The optimization procedure then consists of three separate steps: +\begin_inset Formula +\begin{equation} +x'^{k+1}:=(S^{T}S+\rho I)^{-1}(S^{T}y'+\rho(z'^{k}-u^{k}))\label{eq:optimizex} +\end{equation} + +\end_inset + + +\begin_inset Formula +\[ +z'^{k+1}=S_{(\lambda/\rho)}(x'^{k+1}+u^{k}) +\] + +\end_inset + + +\begin_inset Formula +\[ +u^{k+1}=u^{k}+x'^{k+1}-z'^{k+1} +\] + +\end_inset + +where we have introduced a scalar parameter +\begin_inset Formula $\rho$ +\end_inset + +, a vector +\begin_inset Formula $u$ +\end_inset + +, and a soft thresholding function +\begin_inset Formula $S$ +\end_inset + + (refer to Sec 4.4.3). + These equations implement ADMM in the so-called scaled form, and the converged + solution will not depend on +\begin_inset Formula $\rho$ +\end_inset + +. + [Note that in this version I have changed spectrum function notation from + +\begin_inset Formula $\rho$ +\end_inset + + to +\begin_inset Formula $\mathcal{A}$ +\end_inset + +. + ] The derivations for the above iteration proctocal are shown below. +\end_layout + +\begin_layout Subsection +Scaled form of ADMM +\end_layout + +\begin_layout Standard +We repeat the essentials of the derivation here, following chapter 3. + The ADMM algorithm solves optimization problems of the form +\begin_inset Formula +\[ +\text{{minimize}\ \ }f(x)+g(z) +\] + +\end_inset + + +\begin_inset Formula +\[ +\text{{subject\ to}}\ \ Ax+Bz=c +\] + +\end_inset + +by forming an augmented lagrangian with Lagrangian parameter +\begin_inset Formula $\rho$ +\end_inset + + +\begin_inset Formula +\[ +L_{\rho}(x,z,y)=f(x)+g(z)+y^{T}(Ax+Bz-c)+\frac{{\rho}}{2}||Ax+Bz-c||_{2}^{2} +\] + +\end_inset + +The first two terms are the Lagrangian without the `augmented' constraint. + The remaining part would be zero if the constraint is satisfied. + ADMM then does the iterations: +\begin_inset Formula +\[ +x^{k+1}=\text{argmin}_{x}L_{\rho}(x,z^{k},y^{k}) +\] + +\end_inset + + +\begin_inset Formula +\[ +z^{k+1}=\text{argmin}_{z}L_{\rho}(x^{k+1},z,y^{k}) +\] + +\end_inset + + +\begin_inset Formula +\[ +y^{k+1}=y^{k}+\rho(Ax^{k+1}+Bz^{k+1}-c) +\] + +\end_inset + +This is equivalent to the so-called scaled form, which scales the dual variable + +\begin_inset Formula $y$ +\end_inset + + as +\begin_inset Formula $u=\frac{1}{\rho}y$ +\end_inset + +, such that +\begin_inset Formula +\[ +x^{k+1}=\text{argmin}_{x}\left(f(x)+\frac{\rho}{2}||Ax+Bz^{k}-c+u^{k}||_{2}^{2}\right) +\] + +\end_inset + + +\begin_inset Formula +\[ +z^{k+1}=\text{argmin}_{z}\left(g(z)+\frac{\rho}{2}||Ax^{k+1}+Bz-c+u^{k}||_{2}^{2}\right) +\] + +\end_inset + + +\begin_inset Formula +\[ +u^{k+1}=u^{k}+Ax^{k+1}+Bz^{k+1}-c +\] + +\end_inset + +The vector +\begin_inset Formula $u^{k}$ +\end_inset + + sums up the residuals +\begin_inset Formula $r^{k}=Ax^{k}+Bz^{k}-c$ +\end_inset + +, such that +\begin_inset Formula $u^{k}=u^{0}+\sum_{j=1}^{k}r^{j}$ +\end_inset + +. + The derivations below are switching notations: from +\begin_inset Formula $x$ +\end_inset + +, +\begin_inset Formula $z$ +\end_inset + + to +\begin_inset Formula $x'$ +\end_inset + + and +\begin_inset Formula $z'$ +\end_inset + +. + +\begin_inset Formula $u$ +\end_inset + + stays, but in the code it's also switched to +\begin_inset Formula $u'$ +\end_inset + +. + (In the upcoming code version I will adapt all these notations to match + the codes. + ) +\end_layout + +\begin_layout Subsection +Optimization in +\begin_inset Formula $x'$ +\end_inset + + +\end_layout + +\begin_layout Standard +We start with the description of the optimization in +\begin_inset Formula $x$ +\end_inset + +, which is +\begin_inset Formula $x'^{k+1}=\text{argmin}_{x'}(f(x')+\frac{\rho}{2}||Ax'+Bz'^{k}-c+u^{k}||_{2}^{2})$ +\end_inset + + using +\begin_inset Formula $A=I,$ +\end_inset + + +\begin_inset Formula $B=-I,$ +\end_inset + + +\begin_inset Formula $c=0$ +\end_inset + + or, equivalently, the constraint +\begin_inset Formula $x'-z'=0.$ +\end_inset + + This implies +\begin_inset Formula +\begin{equation} +x'^{k+1}=\text{argmin}_{x'}\left(\frac{1}{2}||Sx'-y'||_{2}^{2}+\frac{\rho}{2}||x'-z'^{k}+u^{k}||_{2}^{2}\right)\label{eq:argmintofind} +\end{equation} + +\end_inset + +Let us multiply this out: +\begin_inset Formula +\[ +\frac{1}{2}\left[(Sx'-y')^{T}(Sx'-y')+\rho(x'-(z'^{k}-u^{k}))^{T}(x'-(z'^{k}-u^{k}))\right]=\frac{{1}}{2}x'^{T}Px'-x'^{T}q+const +\] + +\end_inset + +where +\begin_inset Formula +\[ +P=S^{T}S+\rho I +\] + +\end_inset + + +\begin_inset Formula +\begin{equation} +q=S^{T}(y')+\rho(z'^{k}-u^{k})\label{eq:linearterm} +\end{equation} + +\end_inset + +which has a minimum exactly where +\begin_inset Formula $Px'=q$ +\end_inset + +, or +\begin_inset Formula +\[ +(S^{T}S+\rho I)x'^{+}=S^{T}(y')+\rho(z'^{k}-u^{k}). +\] + +\end_inset + +(where +\begin_inset Formula $v=z'^{k}-u^{k}$ +\end_inset + + p.s. + I don't really know what this +\begin_inset Formula $v$ +\end_inset + + does here, and I think we can just get rid of it here. + p.p.s. + this +\begin_inset Formula $v$ +\end_inset + + is inconsistent with the +\begin_inset Formula $v$ +\end_inset + + definted in the following section. + note that we don't need the constant term to minimize this). + +\end_layout + +\begin_layout Standard +Plugging these expressions back into Eq. + +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:argmintofind" + +\end_inset + +, and writing an explicit inverse rather than an equation solution for +\begin_inset Formula $x'^{k+1}$ +\end_inset + + we obtain +\begin_inset Formula +\[ +x'^{k+1}=(S^{T}S+\rho I)^{-1}(S^{T}y'+\rho(z'^{k}-u^{k})). +\] + +\end_inset + + +\end_layout + +\begin_layout Subsection +Optimization in +\begin_inset Formula $z'$ +\end_inset + + +\end_layout + +\begin_layout Standard +The second optimization is the optimization for the +\begin_inset Formula $L_{1}$ +\end_inset + + term. + It comes from the optimization of +\begin_inset Formula +\[ +z'^{k+1}=\text{argmin}_{z'}\left(g(z')+\frac{\rho}{2}||x'^{k+1}-z'+u^{k}||_{2}^{2}\right)=\text{argmin}_{z'}\left(\lambda|z'|_{1}+\frac{\rho}{2}||z'-(x'^{k+1}+u^{k})||_{2}^{2}\right) +\] + +\end_inset + +where +\begin_inset Formula $g(z')=\lambda|z'|_{1}$ +\end_inset + + and, defining +\begin_inset Formula $v=x'^{k+1}+u^{k}$ +\end_inset + + +\begin_inset Formula +\[ +z'^{k+1}=\text{argmin}_{z'}\left(\lambda|z'|_{1}+\frac{\rho}{2}||z'-v||_{2}^{2}\right) +\] + +\end_inset + +The equation above does not mix different elements of the vector +\begin_inset Formula $z'.$ +\end_inset + + Thus we can rewrite it as an element-wise minimization and do the update + for every element of +\begin_inset Formula $z'$ +\end_inset + + individually, such that +\begin_inset Formula +\[ +z_{j}'^{k+1}=\text{argmin}_{z'_{j}}\left(\lambda|z'_{j}|_{1}+\frac{\rho}{2}(z_{j}'-v_{j})^{2}\right) +\] + +\end_inset + +The solution to this minimization is given by the soft thresholding operator +\begin_inset Formula +\begin{equation} +z_{j}^{'+}=S_{\lambda/\rho}(v_{j})\label{eq:SoftThreshZ} +\end{equation} + +\end_inset + +where the soft thresholding operator +\begin_inset Formula $S$ +\end_inset + + is given by +\begin_inset Formula +\begin{equation} +S_{\kappa}(x)=\begin{cases} +\begin{array}{c} +x-\kappa\\ +0\\ +x+\kappa +\end{array} & \begin{array}{c} +x>\kappa\\ +|x|\leq\kappa\\ +x<-\kappa +\end{array}\end{cases}\label{eq:SoftThresh} +\end{equation} + +\end_inset + +This is derived in detail in chapter 4.4.3. +\end_layout + +\begin_layout Subsection +The soft thresholding function in more detail +\end_layout + +\begin_layout Standard +Notations are getting messy again here, to be fixed. + Here we derive the formula for +\begin_inset Formula $S_{\kappa}(x)$ +\end_inset + + in more detail. + We start by defining the problem as +\begin_inset Formula +\[ +prox_{f}(x)=\text{{argmin}{}_{z}}(\frac{\rho}{2}||z-v||_{2}^{2}+\lambda|z|_{1}) +\] + +\end_inset + +which, because it is separable, we can write as +\begin_inset Formula +\[ +\frac{\partial}{\partial z}(\frac{\rho}{2}(z_{j}-v_{j})^{2}+\lambda|z_{j}|)\overset{!}{=}0 +\] + +\end_inset + +which is +\begin_inset Formula +\[ +z_{j}+\frac{\lambda}{\rho}\frac{\partial}{\partial z_{j}}|z_{j}|=v_{j} +\] + +\end_inset + +if +\begin_inset Formula $|z_{j}|>0,$ +\end_inset + + the derivative is +\begin_inset Formula $1,$ +\end_inset + + if +\begin_inset Formula $|z_{j}|<0$ +\end_inset + +, it is +\begin_inset Formula $-1,$ +\end_inset + + and if +\begin_inset Formula $|z_{j}|=0$ +\end_inset + + we can't really differentiate. + Let's do the case +\begin_inset Formula $z>0$ +\end_inset + + first: +\begin_inset Formula +\[ +z_{j}=v-\frac{\lambda}{\rho}. +\] + +\end_inset + + Otherwise we pick up a +\begin_inset Formula $-1,$ +\end_inset + + and the equation is +\begin_inset Formula +\[ +z_{j}=v+\frac{\lambda}{\rho} +\] + +\end_inset + +Finally let's examine the case of +\begin_inset Formula $|z_{j}|=0.$ +\end_inset + + The literature works with a subdifferential and states +\begin_inset Formula $z_{j}+\frac{\lambda}{\rho}[-1,1]=0,$ +\end_inset + + which has a solution of +\begin_inset Formula $0$ +\end_inset + + for +\begin_inset Formula $z_{j}$ +\end_inset + +in +\begin_inset Formula $[-\frac{\lambda}{\rho},\frac{\lambda}{\rho}].$ +\end_inset + + Putting it all together, we get +\begin_inset Formula +\[ +z_{i}=\begin{cases} +0 & |v_{i}|<\frac{\lambda}{\rho}\\ +v_{i}-\frac{\lambda}{\rho}sgn(v_{i}) & |v_{i}|>\frac{\lambda}{\rho} +\end{cases} +\] + +\end_inset + +This is illustrated in Fig. +\begin_inset CommandInset ref +LatexCommand ref +reference "Fig:SoftThresh" + +\end_inset + +. +\begin_inset Float figure +wide false +sideways false +status collapsed + +\begin_layout Plain Layout + +\end_layout + +\begin_layout Plain Layout +\begin_inset Caption Standard + +\begin_layout Plain Layout +\begin_inset Graphics + filename SoftThresh.pdf + width 5cm + +\end_inset + + +\end_layout + +\end_inset + +This is the soft thresholding function applied to +\begin_inset Formula $x$ +\end_inset + + (in blue) for a threshold of +\begin_inset Formula $2.$ +\end_inset + + Everything moves closer to zero. +\begin_inset CommandInset label +LatexCommand label +name "Fig:SoftThresh" + +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +\end_layout + +\end_inset + +The equations get mildly more interesting if we minimize +\begin_inset Formula +\[ +argmin_{z}\left(\frac{{\rho}}{2}||Ax^{k+1}+Bz-c+u^{k}||_{2}^{2}+\lambda|z|_{1}\right) +\] + +\end_inset + +we then define +\begin_inset Formula +\[ +w=Ax^{k+1}+u^{k}-c +\] + +\end_inset + +and minimize +\begin_inset Formula +\[ +argmin_{z}\left(\frac{\rho}{2}||Bz+w||_{2}^{2}+\lambda|z|_{1}\right)=argmin_{z}\left(\frac{\rho}{2}(z^{T}B^{T}Bz+2z^{T}B^{T}w+w^{T}w)+\lambda|z|_{1}\right) +\] + +\end_inset + +We are only interested here in the case of +\begin_inset Formula $B^{T}B=1,$ +\end_inset + + which allows us to redefine +\begin_inset Formula $v=-B^{T}w$ +\end_inset + + to express the problem as the minimization problem +\begin_inset Formula +\[ +argmin_{z}\left(\frac{\rho}{2}||z-v||_{2}^{2}+\lambda|z|_{1}\right) +\] + +\end_inset + + +\end_layout + +\begin_layout Section +The modification for a positivity constraint +\end_layout + +\begin_layout Standard +We want to enforce positivity of a spectral function. + That means that we want to constrain the fit of +\begin_inset Formula $x'$ +\end_inset + + or +\begin_inset Formula $z'$ +\end_inset + + in such a way that the resulting spectral function is positive everywhere. + In our notation the spectral function is +\begin_inset Formula $\mathcal{A}=Vx'.$ +\end_inset + + We build in this constraint by modifying the Lagrangian from +\begin_inset Formula $L_{\rho}(x',z')$ +\end_inset + + to +\begin_inset Formula +\begin{equation} +L_{\rho}(x',z',s)=f(x')+g(z')+h(s)\label{eq:TripleLagrangian} +\end{equation} + +\end_inset + +i.e. + we introduce a third variable +\begin_inset Formula $s$ +\end_inset + + and alternate the optimization between the three of them, subject to the + constraint that +\begin_inset Formula $x'=z'=V^{T}s$ +\end_inset + +. + +\end_layout + +\begin_layout Standard +In the textbook case, we just have to minimize +\begin_inset Formula $f(x)+h(s).$ +\end_inset + + In that case, +\begin_inset Formula $h(s)$ +\end_inset + + is constructed such that it enforces a positivity constraint such as in + chapter 5, first page, and we obtain +\begin_inset Formula +\[ +s^{k+1}=\Pi_{+}(x^{k+1}+w^{k}) +\] + +\end_inset + +The operator +\begin_inset Formula $\Pi_{+}$ +\end_inset + + is a projection operator onto the domain +\begin_inset Formula $\mathcal{C}$ +\end_inset + + where we want to enforce the values of +\begin_inset Formula $s$ +\end_inset + +, i.e. + here onto the positive domain. + To be concrete, we minimize +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +s^{k+1}=\text{argmin}_{s}(h(s)+\frac{\rho}{2}||x{}^{k+1}-s+w^{k}||_{2}^{2}) +\] + +\end_inset + +with +\begin_inset Formula $h(s)$ +\end_inset + + zero only in +\begin_inset Formula $\mathcal{C}$ +\end_inset + + (we can model it as being infinity outside of +\begin_inset Formula $\mathcal{C}$ +\end_inset + +). + The solution to this is the point where the +\begin_inset Formula $||x^{k+1}-s+w^{k}||$ +\end_inset + + is smallest with +\begin_inset Formula $s$ +\end_inset + + in the domain +\begin_inset Formula $\mathcal{C}$ +\end_inset + +. + In our case of a positivity constraint, the function is minimized for +\begin_inset Formula +\[ +s_{j}=\begin{cases} +0 & (x^{k+1}+w^{k})<0\\ +x^{k+1}+w^{k} & \text{else} +\end{cases} +\] + +\end_inset + +This is also called an Euclidian projection. +\end_layout + +\begin_layout Standard +Back to our case: In the Lagrangian Eq. + +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:TripleLagrangian" + +\end_inset + +, +\begin_inset Formula $h(s)$ +\end_inset + + evaluates to zero if +\begin_inset Formula $s$ +\end_inset + + is positive, and to inifinity otherwise. + We optimize the three constraints in alternating fashion, in two ADMM loops + which independently take care of the optimization of +\begin_inset Formula $z'$ +\end_inset + + and of +\begin_inset Formula $s$ +\end_inset + +: first optimize +\begin_inset Formula $x'$ +\end_inset + + keeping +\begin_inset Formula $z'$ +\end_inset + + and +\begin_inset Formula $s$ +\end_inset + + constant. + Then optimize +\begin_inset Formula $z'$ +\end_inset + + keeping +\begin_inset Formula $x'$ +\end_inset + + constant, and update the running sum of residual +\begin_inset Formula $u'$ +\end_inset + + for this optimization; independently optimize +\begin_inset Formula $s$ +\end_inset + + keeping +\begin_inset Formula $x'$ +\end_inset + + constant, and then update the running residual sum +\begin_inset Formula $w$ +\end_inset + + for that optimization. + +\end_layout + +\begin_layout Standard +If we work with +\begin_inset Formula $s'=V^{T}s$ +\end_inset + + in the singular space: +\begin_inset Formula +\[ +L_{\rho}(x',z',s')=f(x')+g(z')+j(s') +\] + +\end_inset + +and +\begin_inset Formula $j(s')=h(Vs')$ +\end_inset + + is the indicator function evaluated after a transform from singular to + direct space. + The constraint then is that +\begin_inset Formula $x'=z'=s'.$ +\end_inset + + Denoting the running residual vector of the optimization in +\begin_inset Formula $s'$ +\end_inset + + as +\begin_inset Formula $w'$ +\end_inset + +, we obtain +\begin_inset Formula +\[ +s'^{k+1}=V^{T}\Pi_{+}(Vx'^{k+1}+Vw'^{k}) +\] + +\end_inset + +which is satisfied by +\begin_inset Formula $s'=V^{T}s$ +\end_inset + + and (rewriting eq.48) +\begin_inset Formula +\[ +s_{j}=\begin{cases} +0 & Vx'^{k+1}+Vw'^{k}<0\\ +Vx'^{k+1}+Vw'^{k} & \text{else} +\end{cases} +\] + +\end_inset + +After the optimization of +\begin_inset Formula $s'$ +\end_inset + + we need to update the residual vector as +\begin_inset Formula +\[ +w'^{k+1}=w'^{k}+x'^{k+1}-s'^{k+1} +\] + +\end_inset + +which, because it is linear, we can also write in direct space as +\begin_inset Formula +\[ +w^{k+1}=w^{k}+x^{k+1}-s^{k+1} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +Formulating this constraint in direct space rather than in singular space + makes the equations look easier, which is why they probably did it in the + paper. + The only consequence of optimizing multiple constraints is having multiple + residuals in the equation for +\begin_inset Formula $x':$ +\end_inset + + +\begin_inset Formula +\[ +x'^{k+1}=\text{argmin}_{x'}\left(\frac{1}{2}||Sx'-y'||_{2}^{2}+\frac{\rho}{2}||x'-z'^{k}+u^{k}||_{2}^{2}+\frac{\rho'}{2}||x'-s'^{k}+w'{}^{k}||_{2}^{2}\right) +\] + +\end_inset + +multiplying all of this out will lead to additional terms with +\begin_inset Formula $s'$ +\end_inset + +and +\begin_inset Formula $w'$ +\end_inset + + wherever we had terms with +\begin_inset Formula $z'$ +\end_inset + + and +\begin_inset Formula $u$ +\end_inset + +, such that the linear term in the equation for the optimization get modified + to +\begin_inset Formula +\[ +q=S^{T}(y')+\rho(z'^{k}-u^{k})+\rho'(s'^{k}-w'^{k}) +\] + +\end_inset + +The quadratic terms picks up a +\begin_inset Formula $I(\rho+\rho')$ +\end_inset + + where we had an +\begin_inset Formula $I\rho$ +\end_inset + +, and the constant term is irrelevant for the optimization. +\end_layout + +\begin_layout Section +The modification for a norm constraint +\end_layout + +\begin_layout Standard +DEPRECATED. + I THINK THIS IS CLUMSY. +\end_layout + +\begin_layout Standard +In order to have spectral functions with a fixed norm of one, we need to + optimize under the constraint +\begin_inset Formula +\[ +\sum_{j}V_{ji}x'_{i}=1 +\] + +\end_inset + +We do this in just the same way: modify the Lagrangian to +\begin_inset Formula +\[ +L_{\rho}(x',z',s',t')=f(x')+g(z')+j(s')+k(t') +\] + +\end_inset + +where +\begin_inset Formula $k(t')=\nu(\langle Vt'\rangle-1)$ +\end_inset + + and, as in the paper, +\begin_inset Formula $\langle\cdot\rangle$ +\end_inset + +denotes the integral over the spectral function, which we can also write + as +\begin_inset Formula $\langle x\rangle=e\cdot x$ +\end_inset + +, where the vector +\begin_inset Formula $e$ +\end_inset + +is a unit vector chosen such that +\begin_inset Formula $\int d\omega A(\omega)\approx\sum_{j}x_{j}$ +\end_inset + +. + As a consequence, we pick up yet another optimization step and yet another + vector of residuals +\begin_inset Formula $v',$ +\end_inset + + such that +\begin_inset Formula +\[ +x'^{k+1}=\text{argmin}_{x}(\frac{1}{2}||Sx'-y'^{k}||_{2}^{2}+\frac{\rho}{2}||x'-z'^{k}+u^{k}||_{2}^{2}+\frac{\rho'}{2}||x'-s'^{k}+w'^{k}||+\frac{\rho''}{2}||x'-t'^{k}+v'^{k}||) +\] + +\end_inset + +this will modify the quadratic part of the optimization to +\begin_inset Formula +\begin{equation} +A=S^{T}S+(\rho+\rho'+\rho'')I\label{eq:AWithTwoConstraints} +\end{equation} + +\end_inset + +and change the linear part to +\begin_inset Formula +\[ +b=S^{T}(y'^{k})-\rho(z'^{k}-u^{k})-\rho'(w'^{k}-s'^{k})-\rho''(v'^{k}-t'^{k}) +\] + +\end_inset + +and it will require an additional step for the optimization of +\begin_inset Formula $t$ +\end_inset + + and an update of the residuals +\begin_inset Formula $v.$ +\end_inset + + The +\begin_inset Formula $t$ +\end_inset + + update is given as +\begin_inset Formula +\[ +t'^{k+1}=\text{argmin}_{t'}(k(t')-\frac{\rho''}{2}||x'{}^{k+1}-t'+v'^{k}||_{2}^{2}) +\] + +\end_inset + +and we can write this as the optmization of a quadratic equation, similar + to the optimization of +\begin_inset Formula $x'$ +\end_inset + +, and obtain the quadratic and linear terms +\begin_inset Formula +\[ +t'^{k+1}=\text{argmin}_{t'}\frac{-\rho''}{2}t'^{T}t'-(\rho''(x'^{k+1}+v^{'k})^{T}+\nu eV)t'+const +\] + +\end_inset + +which results in +\begin_inset Formula +\begin{equation} +t'^{k+1}=(x'+v'^{k})+\frac{\nu}{\rho''}eV\label{eq:normeq} +\end{equation} + +\end_inset + +this needs to be followed by an update of the running residuals, +\begin_inset Formula +\begin{equation} +v'^{k+1}=v'^{k}+x'^{k+1}-t'^{k}\label{eq:normrunres} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Section +The modification for high frequency constraints +\end_layout + +\begin_layout Standard +This is not in the paper, but it is a straightforward extension of the constrain +ts in the paper. + We have additional constraints for the spectral functions, which are +\begin_inset Formula +\[ +c_{2}=\int\omega A(\omega) +\] + +\end_inset + + +\begin_inset Formula +\[ +c_{3}=\int\omega^{2}A(\omega) +\] + +\end_inset + +These constraints come straight out of the series expansion of +\begin_inset Formula $G(i\omega_{n})=\frac{{1}}{i\omega_{n}}+\frac{c_{2}}{(i\omega_{n})^{2}}+\frac{c_{3}}{(i\omega_{n})^{3}}+...$ +\end_inset + + and the evaluation of the kernel. +\begin_inset Formula +\[ +n=\int A(\omega)f_{\beta}(\omega-\mu) +\] + +\end_inset + +This is just the expression for the particle number. + Frequently we know these terms analytically, or we at least know then to + much higher precision than the spectral function. + They can be enforced using a constraint just as the norm constraint. +\end_layout + +\begin_layout Section +Building in norm, integral and positivity constraints exactly +\end_layout + +\begin_layout Standard +\noindent +ADMM has a straightforward way of building in constraints: currently we + use +\begin_inset Formula $x'=z'$ +\end_inset + +, or +\begin_inset Formula $Ax'+Bz'-c=0$ +\end_inset + + with +\begin_inset Formula $A=I$ +\end_inset + + and +\begin_inset Formula $B=-I$ +\end_inset + + and +\begin_inset Formula $c=0.$ +\end_inset + + A, B, and c do not need to be +\begin_inset Formula $n_{s}\times n_{s}$ +\end_inset + + matrices and it should be easy to extend +\begin_inset Formula $A$ +\end_inset + +, +\begin_inset Formula $B$ +\end_inset + +, and +\begin_inset Formula $c$ +\end_inset + + by a row each, such that +\begin_inset Formula +\begin{equation} +A=\left(\begin{array}{c} +I_{n_{s}}\\ +\sum_{j}V_{jk} +\end{array}\right)\label{eq:AWithNorm} +\end{equation} + +\end_inset + + +\begin_inset Formula +\[ +B=\left(\begin{array}{c} +-I_{n_{s}}\\ +0 +\end{array}\right) +\] + +\end_inset + + +\begin_inset Formula +\[ +c=\left(\begin{array}{c} +0\\ +1 +\end{array}\right) +\] + +\end_inset + +such that the last line enforces +\begin_inset Formula +\[ +\sum_{j}V_{jk}x'_{k}=1 +\] + +\end_inset + +which is the condition for the norm. + This will leave the +\begin_inset Formula $L_{1}$ +\end_inset + + optimization of +\begin_inset Formula $z'$ +\end_inset + + invariant but will change the optimization for +\begin_inset Formula $x'$ +\end_inset + + to +\begin_inset Formula +\[ +x'^{k+1}=\text{argmin}_{x'}\left(\frac{1}{2}||Sx'-y'||_{2}^{2}+\frac{\rho}{2}||Ax'+Bz'^{k}-c+u^{k}||_{2}^{2}\right) +\] + +\end_inset + +Multiplying this out, we get a quadratic equation of the form +\begin_inset Formula $\frac{1}{2}x^{T}Px-q^{T}x+c=0$ +\end_inset + + , with a solution at +\begin_inset Formula $Px=q$ +\end_inset + +, for +\begin_inset Formula +\begin{equation} +P=S^{T}S+\rho A^{T}A\label{eq:PofQuadEqWithNorm} +\end{equation} + +\end_inset + + +\begin_inset Formula +\begin{equation} +q=y'^{T}S-\rho(Bz'^{k}-c+u^{k})^{T}A\label{eq:qofQuadEqWithNorm} +\end{equation} + +\end_inset + +Additional constraints for +\begin_inset Formula $\int d\omega\omega A(\omega)$ +\end_inset + + and +\begin_inset Formula $\int d\omega\omega^{2}A(\omega)$ +\end_inset + + result in additional lines with +\begin_inset Formula $\sum_{j}\omega_{j}V_{jk}$ +\end_inset + + and +\begin_inset Formula $\sum_{j}\omega_{j}^{2}V_{jk}$ +\end_inset + + for +\begin_inset Formula $A$ +\end_inset + + and +\begin_inset Formula $c_{2}$ +\end_inset + + and +\begin_inset Formula $c_{3}$ +\end_inset + + for +\begin_inset Formula $c.$ +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +\align left +If positivity constraint needs to be implemented, the optimization for +\begin_inset Formula $x'$ +\end_inset + + takes a modified form, with +\begin_inset Formula $\rho'$ +\end_inset + + term added: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +x'^{k+1}=\text{argmin}_{x'}\left(\frac{1}{2}||Sx'-y'||_{2}^{2}+\frac{\rho}{2}||Ax'+Bz'^{k}-c+u^{k}||_{2}^{2}+\frac{\rho'}{2}||x'-s'^{k}+w'{}^{k}||_{2}^{2}\right) +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +\align left +The quadratic equation remains its form +\begin_inset Formula $\frac{1}{2}x^{T}Px-q^{T}x+c=0$ +\end_inset + +, with +\begin_inset Formula $P$ +\end_inset + + and +\begin_inset Formula $q$ +\end_inset + + modified as shown in the following section. + +\end_layout + +\begin_layout Section +Summary of Equations +\end_layout + +\begin_layout Standard +This section summarizes the equations needed to solve the ADMM problem. + We start with the calculation of +\begin_inset Formula $A$ +\end_inset + + and +\begin_inset Formula $B$ +\end_inset + + as in +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:AWithNorm" + +\end_inset + + and the full optimization, including positivity, of +\begin_inset Formula $x^{k+1}$ +\end_inset + + according to Eq. +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:PofQuadEqWithNorm" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:qofQuadEqWithNorm" + +\end_inset + +. +\begin_inset Formula +\begin{align} +P & =S^{T}S+\rho A^{T}A+\rho'I\\ +q & =y'^{T}S-\rho(Bz'{}^{k}-c+u^{k})^{T}A-\rho'(w'^{k}-s'^{k})\\ +Px'^{k+1} & =q +\end{align} + +\end_inset + +As the matrix +\begin_inset Formula $A$ +\end_inset + + is diagonal, we can replace the last equation by an element-wise division + of +\begin_inset Formula $b$ +\end_inset + + by +\begin_inset Formula $A.$ +\end_inset + + We then update the +\begin_inset Formula $L_{1}$ +\end_inset + + norm and its dual variable according to Eq. + +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:SoftThreshZ" + +\end_inset + + and Eq. + +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:SoftThresh" + +\end_inset + +. + This will take care of +\begin_inset Formula $z'$ +\end_inset + + and its running residual +\begin_inset Formula $u$ +\end_inset + +. +\begin_inset Formula +\begin{align} +z'^{k+1} & =S_{\lambda/\rho}(x'^{k+1}+u^{k})\\ +u^{k+1} & =u^{k}+Ax'^{k+1}+Bz'^{k+1}-c +\end{align} + +\end_inset + +We then satisfy all other constraints, starting with the positivity, variables + +\begin_inset Formula $s'$ +\end_inset + + and +\begin_inset Formula $w'$ +\end_inset + +: +\begin_inset Formula +\begin{align} +s'^{k+1} & =V^{T}\Pi_{+}(Vx'^{k+1}+Vw'^{k})\\ +w'^{k+1} & =w'^{k}+x'^{k+1}-s'^{k+1} +\end{align} + +\end_inset + + +\end_layout + +\end_body +\end_document